files / problems / brocard / compute / q2-results.json

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{
  "range_inclusive": [
    4,
    100
  ],
  "method": "exact meet-in-the-middle enumeration of unitary divisors of n!/4; the largest divisor at most sqrt(n!/4) gives the minimum gap",
  "source_sha256": "69ea4edb5206d59010900f273d15236e47d779de68232680fc92c23c6ac90b50",
  "structural_solutions": [
    {
      "n": 4,
      "m": 5,
      "a": 2,
      "b": 3,
      "odd_prime_power_signs": [
        {
          "prime": 3,
          "modulus": "3",
          "congruence": "-1"
        }
      ]
    },
    {
      "n": 5,
      "m": 11,
      "a": 5,
      "b": 6,
      "odd_prime_power_signs": [
        {
          "prime": 3,
          "modulus": "3",
          "congruence": "-1"
        },
        {
          "prime": 5,
          "modulus": "5",
          "congruence": "+1"
        }
      ]
    },
    {
      "n": 7,
      "m": 71,
      "a": 35,
      "b": 36,
      "odd_prime_power_signs": [
        {
          "prime": 3,
          "modulus": "9",
          "congruence": "-1"
        },
        {
          "prime": 5,
          "modulus": "5",
          "congruence": "+1"
        },
        {
          "prime": 7,
          "modulus": "7",
          "congruence": "+1"
        }
      ]
    }
  ],
  "direct_square_solutions": [
    {
      "n": 4,
      "m": 5
    },
    {
      "n": 5,
      "m": 11
    },
    {
      "n": 7,
      "m": 71
    }
  ],
  "methods_agree": true,
  "records": [
    {
      "n": 4,
      "prime_power_block_count": 2,
      "sign_vectors_up_to_swap": "2",
      "closest_a": "2",
      "closest_b": "3",
      "gap": "1",
      "log10_gap": 0.0,
      "small_factor_primes": [
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      "large_factor_primes": [
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      "is_consecutive": true
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    {
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      "is_consecutive": true
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