{
  "status": "PASS",
  "runs": [
    {
      "k": 2,
      "sign": -1,
      "complete_for_this_k": true,
      "stop_reason": null,
      "M_upper_bound": 1,
      "limits": {
        "nodes": 500000,
        "prime_upper": 300000,
        "trial_divisor": 1000000
      },
      "statistics": {
        "nodes": 0,
        "prime_choices": 0,
        "integer_tail_candidates": 0,
        "tail_primality_tests": 0,
        "maximum_next_prime_bound": 0
      },
      "solutions": [],
      "scope": "Only this specified k. No inference that all k have been checked.",
      "full_lehmer_conjecture_proved": false
    },
    {
      "k": 3,
      "sign": -1,
      "complete_for_this_k": true,
      "stop_reason": null,
      "M_upper_bound": 2,
      "limits": {
        "nodes": 500000,
        "prime_upper": 300000,
        "trial_divisor": 1000000
      },
      "statistics": {
        "nodes": 1,
        "prime_choices": 0,
        "integer_tail_candidates": 0,
        "tail_primality_tests": 0,
        "maximum_next_prime_bound": 3
      },
      "solutions": [],
      "scope": "Only this specified k. No inference that all k have been checked.",
      "full_lehmer_conjecture_proved": false
    },
    {
      "k": 4,
      "sign": -1,
      "complete_for_this_k": true,
      "stop_reason": null,
      "M_upper_bound": 2,
      "limits": {
        "nodes": 500000,
        "prime_upper": 300000,
        "trial_divisor": 1000000
      },
      "statistics": {
        "nodes": 1,
        "prime_choices": 0,
        "integer_tail_candidates": 0,
        "tail_primality_tests": 0,
        "maximum_next_prime_bound": 4
      },
      "solutions": [],
      "scope": "Only this specified k. No inference that all k have been checked.",
      "full_lehmer_conjecture_proved": false
    },
    {
      "k": 5,
      "sign": -1,
      "complete_for_this_k": true,
      "stop_reason": null,
      "M_upper_bound": 3,
      "limits": {
        "nodes": 500000,
        "prime_upper": 300000,
        "trial_divisor": 1000000
      },
      "statistics": {
        "nodes": 4,
        "prime_choices": 2,
        "integer_tail_candidates": 0,
        "tail_primality_tests": 0,
        "maximum_next_prime_bound": 8
      },
      "solutions": [],
      "scope": "Only this specified k. No inference that all k have been checked.",
      "full_lehmer_conjecture_proved": false
    },
    {
      "k": 6,
      "sign": -1,
      "complete_for_this_k": true,
      "stop_reason": null,
      "M_upper_bound": 3,
      "limits": {
        "nodes": 500000,
        "prime_upper": 300000,
        "trial_divisor": 1000000
      },
      "statistics": {
        "nodes": 4,
        "prime_choices": 2,
        "integer_tail_candidates": 0,
        "tail_primality_tests": 0,
        "maximum_next_prime_bound": 11
      },
      "solutions": [],
      "scope": "Only this specified k. No inference that all k have been checked.",
      "full_lehmer_conjecture_proved": false
    },
    {
      "k": 7,
      "sign": -1,
      "complete_for_this_k": true,
      "stop_reason": null,
      "M_upper_bound": 3,
      "limits": {
        "nodes": 500000,
        "prime_upper": 300000,
        "trial_divisor": 1000000
      },
      "statistics": {
        "nodes": 5,
        "prime_choices": 3,
        "integer_tail_candidates": 0,
        "tail_primality_tests": 0,
        "maximum_next_prime_bound": 15
      },
      "solutions": [],
      "scope": "Only this specified k. No inference that all k have been checked.",
      "full_lehmer_conjecture_proved": false
    },
    {
      "k": 8,
      "sign": -1,
      "complete_for_this_k": true,
      "stop_reason": null,
      "M_upper_bound": 4,
      "limits": {
        "nodes": 500000,
        "prime_upper": 300000,
        "trial_divisor": 1000000
      },
      "statistics": {
        "nodes": 11,
        "prime_choices": 8,
        "integer_tail_candidates": 0,
        "tail_primality_tests": 0,
        "maximum_next_prime_bound": 26
      },
      "solutions": [],
      "scope": "Only this specified k. No inference that all k have been checked.",
      "full_lehmer_conjecture_proved": false
    },
    {
      "k": 9,
      "sign": -1,
      "complete_for_this_k": true,
      "stop_reason": null,
      "M_upper_bound": 4,
      "limits": {
        "nodes": 500000,
        "prime_upper": 300000,
        "trial_divisor": 1000000
      },
      "statistics": {
        "nodes": 17,
        "prime_choices": 14,
        "integer_tail_candidates": 0,
        "tail_primality_tests": 0,
        "maximum_next_prime_bound": 40
      },
      "solutions": [],
      "scope": "Only this specified k. No inference that all k have been checked.",
      "full_lehmer_conjecture_proved": false
    },
    {
      "k": 10,
      "sign": -1,
      "complete_for_this_k": true,
      "stop_reason": null,
      "M_upper_bound": 4,
      "limits": {
        "nodes": 500000,
        "prime_upper": 300000,
        "trial_divisor": 1000000
      },
      "statistics": {
        "nodes": 26,
        "prime_choices": 23,
        "integer_tail_candidates": 0,
        "tail_primality_tests": 0,
        "maximum_next_prime_bound": 62
      },
      "solutions": [],
      "scope": "Only this specified k. No inference that all k have been checked.",
      "full_lehmer_conjecture_proved": false
    },
    {
      "k": 11,
      "sign": -1,
      "complete_for_this_k": true,
      "stop_reason": null,
      "M_upper_bound": 4,
      "limits": {
        "nodes": 500000,
        "prime_upper": 300000,
        "trial_divisor": 1000000
      },
      "statistics": {
        "nodes": 59,
        "prime_choices": 56,
        "integer_tail_candidates": 0,
        "tail_primality_tests": 0,
        "maximum_next_prime_bound": 116
      },
      "solutions": [],
      "scope": "Only this specified k. No inference that all k have been checked.",
      "full_lehmer_conjecture_proved": false
    },
    {
      "k": 2,
      "sign": 1,
      "complete_for_this_k": true,
      "stop_reason": null,
      "M_upper_bound": 2,
      "limits": {
        "nodes": 500000,
        "prime_upper": 300000,
        "trial_divisor": 1000000
      },
      "statistics": {
        "nodes": 2,
        "prime_choices": 1,
        "integer_tail_candidates": 1,
        "tail_primality_tests": 1,
        "maximum_next_prime_bound": 4
      },
      "solutions": [
        {
          "factors": [
            3,
            5
          ],
          "n": 15,
          "phi": 8,
          "M": 2
        }
      ],
      "scope": "Only this specified k. No inference that all k have been checked.",
      "full_lehmer_conjecture_proved": false
    },
    {
      "k": 3,
      "sign": 1,
      "complete_for_this_k": true,
      "stop_reason": null,
      "M_upper_bound": 3,
      "limits": {
        "nodes": 500000,
        "prime_upper": 300000,
        "trial_divisor": 1000000
      },
      "statistics": {
        "nodes": 5,
        "prime_choices": 3,
        "integer_tail_candidates": 1,
        "tail_primality_tests": 1,
        "maximum_next_prime_bound": 8
      },
      "solutions": [
        {
          "factors": [
            3,
            5,
            17
          ],
          "n": 255,
          "phi": 128,
          "M": 2
        }
      ],
      "scope": "Only this specified k. No inference that all k have been checked.",
      "full_lehmer_conjecture_proved": false
    },
    {
      "k": 4,
      "sign": 1,
      "complete_for_this_k": true,
      "stop_reason": null,
      "M_upper_bound": 3,
      "limits": {
        "nodes": 500000,
        "prime_upper": 300000,
        "trial_divisor": 1000000
      },
      "statistics": {
        "nodes": 9,
        "prime_choices": 7,
        "integer_tail_candidates": 1,
        "tail_primality_tests": 1,
        "maximum_next_prime_bound": 32
      },
      "solutions": [
        {
          "factors": [
            3,
            5,
            17,
            257
          ],
          "n": 65535,
          "phi": 32768,
          "M": 2
        }
      ],
      "scope": "Only this specified k. No inference that all k have been checked.",
      "full_lehmer_conjecture_proved": false
    },
    {
      "k": 5,
      "sign": 1,
      "complete_for_this_k": true,
      "stop_reason": null,
      "M_upper_bound": 4,
      "limits": {
        "nodes": 500000,
        "prime_upper": 300000,
        "trial_divisor": 1000000
      },
      "statistics": {
        "nodes": 35,
        "prime_choices": 32,
        "integer_tail_candidates": 2,
        "tail_primality_tests": 2,
        "maximum_next_prime_bound": 512
      },
      "solutions": [
        {
          "factors": [
            3,
            5,
            17,
            353,
            929
          ],
          "n": 83623935,
          "phi": 41811968,
          "M": 2
        },
        {
          "factors": [
            3,
            5,
            17,
            257,
            65537
          ],
          "n": 4294967295,
          "phi": 2147483648,
          "M": 2
        }
      ],
      "scope": "Only this specified k. No inference that all k have been checked.",
      "full_lehmer_conjecture_proved": false
    },
    {
      "k": 6,
      "sign": 1,
      "complete_for_this_k": true,
      "stop_reason": null,
      "M_upper_bound": 4,
      "limits": {
        "nodes": 500000,
        "prime_upper": 300000,
        "trial_divisor": 1000000
      },
      "statistics": {
        "nodes": 3403,
        "prime_choices": 3400,
        "integer_tail_candidates": 3,
        "tail_primality_tests": 3,
        "maximum_next_prime_bound": 131072
      },
      "solutions": [
        {
          "factors": [
            3,
            5,
            17,
            353,
            929,
            83623937
          ],
          "n": 6992962672132095,
          "phi": 3496481336066048,
          "M": 2
        }
      ],
      "scope": "Only this specified k. No inference that all k have been checked.",
      "full_lehmer_conjecture_proved": false
    }
  ],
  "independent_small_tuple_comparisons": 1254,
  "known_companion_solutions_reproduced": 6,
  "known_solution_prefix_cutoffs_checked": 19,
  "resource_stop_negative_control": "PASS",
  "all_k_exclusion_proved": false,
  "uniform_construction_proof": "Written theorem; not inferred from tests."
}