{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1203",
  "content_hash": null,
  "slug": "erdos-problem-141-attempt-resolution-route",
  "type": "attempt",
  "title": "Resolve the stated acceptance condition",
  "summary": "Give a rigorous proof or counterexample that completely resolves this statement: Erdős Problem 141: For every integer \\(k \\geq 3\\), does there exist a set of \\(k\\) consecutive primes in arithmetic progression? That is, for each \\(k \\geq 3\\), does there exist a set \\(s\\) of natural numbers such that \\(s\\) forms an arithmetic progression of length \\(k\\) and consists of \\(k\\) consecutive primes?",
  "relevance": "For Consecutive Primes in Arithmetic Progression, record erdos-problem-141-attempt-resolution-route (“Resolve the stated acceptance condition”) documents a concrete method, search boundary, or failed route. The record states: Give a rigorous proof or counterexample that completely resolves this statement: Erdős Problem 141: For every integer \\(k \\geq 3\\), does there exist a set of \\(k\\) consecutive primes in arithmetic progression?",
  "relevance_source": "recorded",
  "body": "Target the displayed statement directly. Give a rigorous proof or counterexample that completely resolves this statement: Erdős Problem 141: For every integer \\(k \\geq 3\\), does there exist a set of \\(k\\) consecutive primes in arithmetic progression? That is, for each \\(k \\geq 3\\), does there exist a set \\(s\\) of natural numbers such that \\(s\\) forms an arithmetic progression of length \\(k\\) and consists of \\(k\\) consecutive primes? Preserve exact hypotheses, source locators, and any finite certificates so later work can distinguish a full resolution from partial progress.",
  "status": "open_strategy",
  "evidence_grade": "self_reported",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://www.erdosproblems.com/141",
      "locator": "Editorial research route recorded 2026-07-31"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://www.erdosproblems.com/141",
    "locator": "Editorial research route recorded 2026-07-31"
  },
  "models": [],
  "relations": [
    {
      "slug": "R1204",
      "title": "Current status and unresolved remainder",
      "object_type": "claim",
      "relation": "addresses",
      "direction": "outgoing"
    },
    {
      "slug": "erdos-problem-141",
      "title": "erdos problem 141",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}