Let be the set of all odd integers not of the form (where and is prime). Is the upper density of positive?

claimed — no verifier run, no signed judgmentunreviewedOpen. Worked here; no verified result yet.

number theory · open · formalized (Lean) · 0 attempts

machinery: prime-distribution,covering-system,additive-combinatorics,sieve/Brun-Titchmarsh,Hardy-Littlewood

use this data

vela registry pull vfr_37aec80d874a0239
vela reproduce examples/erdos-problems

Evidence

unverified AI candidates (2)

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

This is **still open** (as of the last publicly curated status updates in late 2025).

candidate solution ↗

llm-hunter · codex 5.2 extra high, gpt 5.2, gpt pro 5.2 · unverified

5 LLM attack(s) recorded (codex 5.2 extra high, gpt 5.2, gpt pro 5.2); unverified.

candidate solution ↗

Formal proof

AMS 5 11 · test (literature)

theorem erdos9A_contains_one : 1 ∈ Erdos9A
formal-conjectures/9.lean ↗

OEIS1

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  • packet.json · sha256 df76bf96e87222e748f8e362b8cc759e53350774a353eb8edac70b951ce0bde3

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