Let $A$ be the set of all odd integers $\geq 1$ not of the form $p + 2^{k} + 2^{l}$ (where $k, l \geq 0$ and $p$ is prime). Is the upper density of $A$ positive?

Worked, still open.

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

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

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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).

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.

AMS 5 11 · test (literature)

theorem erdos9A_contains_one : 1 ∈ Erdos9A

open