{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1572",
  "content_hash": null,
  "slug": "goldbach-conjecture-status-packet-quality-20260801",
  "type": "claim",
  "title": "Dated status and exact unresolved remainder",
  "summary": "Unresolved in this packet after the dated source check. Strongest checked result: Oliveira e Silva, Herzog, and Pardi verified the binary Goldbach conjecture for every even integer up to 4 × 10^18. Chen proved that every sufficiently large even integer is the sum of a prime and an integer with at most two prime factors. The binary conjecture for all even integers remains open. Exact unresolved remainder: Prove that every even integer greater than 2 is a sum of two primes, or exhibit an even integer and prove that no such pair exists.",
  "relevance": "For Goldbach conjecture, this successor gives readable dated status prose and the exact remaining research boundary.",
  "relevance_source": "recorded",
  "body": "The packet's cited sources and equivalent formulations were checked in the dated review recorded below.\n\nStrongest checked result: Oliveira e Silva, Herzog, and Pardi verified the binary Goldbach conjecture for every even integer up to 4 × 10^18. Chen proved that every sufficiently large even integer is the sum of a prime and an integer with at most two prime factors. The binary conjecture for all even integers remains open.\n\nExact unresolved remainder: Prove that every even integer greater than 2 is a sum of two primes, or exhibit an even integer and prove that no such pair exists.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/2501.02529",
      "locator": "abstract and introduction's Goldbach formulation"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2501.02529",
    "locator": "abstract and introduction's Goldbach formulation"
  },
  "models": [],
  "relations": [
    {
      "slug": "R1068",
      "title": "Current status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing"
    },
    {
      "slug": "goldbach-conjecture",
      "title": "goldbach conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}