erdos_699_index_12_complete.json

{
  "i": 12,
  "supplied_tail_power_of_ten": 3071170,
  "inclusive_interval_cap_power_of_ten": 43,
  "terminal_prime_lower_row": 113,
  "coarse_cofactor_saving_scaled": 13332,
  "visited_intervals": 299881,
  "certified_intervals": 149926,
  "intervals_requiring_prime_pairs": 66631,
  "total_partition_leaves": 149941,
  "minimum_certified_log_margin": "0.0000324453138194694737278643350190600836756104925363993447",
  "interval_partition_sha256": "c5fe8a3d0ea7e05843af22f355f5c994cbb3a0c05340a08dd5baa8ba60c383e9",
  "active_cofactor_graphs_used": 103,
  "finite_pair_constraints": 20,
  "exceptional_row_windows": 209,
  "exact_singleton_rows": [
    736,
    352,
    256,
    253,
    252,
    251,
    250,
    245,
    200,
    136,
    135,
    132,
    130,
    129,
    128
  ],
  "exact_columns_checked": 1610,
  "source_certificates": [
    {
      "file": "erdos_699_prime_pair_strips_15.json"
    },
    {
      "file": "erdos_699_prime_pair_strips_12.json"
    }
  ],
  "gap_data_file": "erdos_699_prime_gap_records.json",
  "conclusion": "No admissible bad triples exist at index twelve.",
  "numerical_tail_file": "erdos_699_off_diagonal_explicit_pairs.json",
  "weighted_ramp_reduction": {
    "i": 12,
    "k": 8,
    "primes": [
      2,
      3,
      5,
      7,
      11
    ],
    "degree": 72,
    "total_multiplicity": 126,
    "weighted_moment": 550,
    "minimal_vector_count": 5,
    "capacity_configurations_checked": 35,
    "minimum_gain": "9991/5000",
    "worst_vector_scaled": [
      0,
      3333,
      3333,
      3333,
      3333
    ],
    "worst_row_capacities_scaled": [
      10000,
      6667,
      6667,
      6667,
      6667
    ],
    "off_maximum_factors": [
      {
        "prime": 2,
        "exponent": 102,
        "maximizing_positions": [
          8
        ]
      },
      {
        "prime": 3,
        "exponent": 55,
        "maximizing_positions": [
          9
        ]
      },
      {
        "prime": 5,
        "exponent": 27,
        "maximizing_positions": [
          10
        ]
      },
      {
        "prime": 7,
        "exponent": 16,
        "maximizing_positions": [
          7
        ]
      },
      {
        "prime": 11,
        "exponent": 16,
        "maximizing_positions": [
          11
        ]
      }
    ],
    "rough_denominator": 1,
    "elementary_threshold": 1430000,
    "algebraic_cap_power_of_ten": 43,
    "source_threshold": "The retained finite five-prime clique of exponent 1/3.",
    "full_bound": "max(10^43, The retained finite five-prime clique of exponent 1/3.)"
  }
}