Erdős problems frontier

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  "text": "Erdős Problem #489 remains OPEN. Statement: Let $A\\subseteq \\mathbb{N}$ be a set such that $\\lvert A\\cap [1,x]\\rvert=o(x^{1/2})$. Let $B=\\{ n\\geq 1 : a\\nmid n\\textrm{ for all }a\\in A\\}$. If $B=\\{b_1 < b_2 < \\cdots\\}$ then is it true that $$\\lim_{x \\to \\infty} \\frac{1}{x}\\sum_{b_i < x}(b_{i+1}-b_i)^2$$ exists (and is finite)? For example, when $A=\\{p^2: p\\textrm{ prime}\\}$ then $B$ is the set of squarefree numbers, and the existence of this limit was proved by Erdős. See also [208]. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.",
  "type": "open_question"
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  "text": "Agent-imported candidate claim; scope requires review."
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  "kind": "frontier_epistemic",
  "method": "expert_judgment",
  "score": 0.99
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 "created": "2026-05-30T00:42:06.826507+00:00",
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 "provenance": {
  "authors": [
   {
    "name": "Erdős Open-Problem spine ingest",
    "orcid": null
   }
  ],
  "citation_count": null,
  "doi": null,
  "extraction": {
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   "model": "agent:erdos-spine-ingest",
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  "source_type": "model_output",
  "title": "cap_61973ee16b553d57 · vc_894bfe319d3806af",
  "url": "https://www.erdosproblems.com/489",
  "year": null
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}