{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R683",
  "content_hash": null,
  "slug": "rsg-claim-witness-30922-30929",
  "type": "claim",
  "title": "The interval 30,922 to 30,929 has a six-color square-prime certificate",
  "summary": "Exact factorizations prove both endpoints squarefree and label the six interior integers by 17, 3, 5, 47, 13, and 2.",
  "relevance": "For Largest rainbow squarefree gap below 10^12, record rsg-claim-witness-30922-30929 (“The interval 30,922 to 30,929 has a six-color square-prime certificate”) records a bound, answer, status fact, or structural consequence. The record states: Exact factorizations prove both endpoints squarefree and label the six interior integers by 17, 3, 5, 47, 13, and 2.",
  "relevance_source": "recorded",
  "body": "The endpoint factorizations are\n\\[\n30922=2\\cdot15461,\n\\qquad\n30929=157\\cdot197,\n\\]\nand every displayed factor is prime. Thus both endpoints are squarefree.\n\nThe interior factorizations are\n\\[\n\\begin{aligned}\n30923&=17^2\\cdot107,\\\\\n30924&=2^2\\cdot3^2\\cdot859,\\\\\n30925&=5^2\\cdot1237,\\\\\n30926&=2\\cdot7\\cdot47^2,\\\\\n30927&=3\\cdot13^2\\cdot61,\\\\\n30928&=2^4\\cdot1933.\n\\end{aligned}\n\\]\nAssigning the primes\n\\[\n(17,3,5,47,13,2)\n\\]\nin increasing order of the interior integers gives six distinct labels, each with its square dividing the corresponding integer.",
  "status": "established",
  "evidence_grade": "mathematical_identity",
  "scope": {
    "kind": "bounded",
    "statement": "the single interval with endpoints 30922 and 30929",
    "bounds": {
      "a": {
        "min": 30922,
        "max": 30922
      },
      "b": {
        "min": 30929,
        "max": 30929
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/1912.04972",
      "locator": "Exact integer factorizations replayed in rsg-artifact-prefix-sieve-five-million"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1912.04972",
    "locator": "Exact integer factorizations replayed in rsg-artifact-prefix-sieve-five-million"
  },
  "relations": [
    {
      "slug": "R679",
      "title": "Exact square-divisor sieve and matching replay through five million",
      "object_type": "artifact",
      "relation": "verifies",
      "direction": "incoming"
    },
    {
      "slug": "R682",
      "title": "The exact rainbow maximum through five million is 7",
      "object_type": "claim",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "rainbow-squarefree-gap-1e12",
      "title": "rainbow squarefree gap 1e12",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}