{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1084",
  "content_hash": null,
  "slug": "infinitely-many-mersenne-primes-claim-status-20260731",
  "type": "claim",
  "title": "Current status and unresolved remainder",
  "summary": "The cited AMS article identifies the infinitude of Mersenne primes as unresolved, and current public status was checked on 2026-07-31. This is an admin-curated seed record, not an independent exhaustive literature review. Prove that infinitely many prime exponents p give 2^p - 1 prime, or prove that only finitely many do.",
  "relevance": "Defines the dated frontier and the exact remainder that research on this problem must resolve.",
  "relevance_source": "recorded",
  "body": "The cited AMS article identifies the infinitude of Mersenne primes as unresolved, and current public status was checked on 2026-07-31. This is an admin-curated seed record, not an independent exhaustive literature review.\n\nA complete resolution must satisfy this condition: Prove that infinitely many prime exponents p give 2^p - 1 prime, or prove that only finitely many do.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://blogs.ams.org/mathgradblog/2013/07/18/infinitude-mersenne-primes/",
      "locator": "See dataset.references[0] for the exact external source and locator."
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://blogs.ams.org/mathgradblog/2013/07/18/infinitude-mersenne-primes/",
    "locator": "See dataset.references[0] for the exact external source and locator."
  },
  "relations": [
    {
      "slug": "R1083",
      "title": "Resolve the stated acceptance condition",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "R1610",
      "title": "Dated status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "incoming"
    },
    {
      "slug": "infinitely-many-mersenne-primes",
      "title": "infinitely many mersenne primes",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}