Let$$f(n)=\underset{i<n}{\min }(p_{n+i}+p_{n-i}),$$where $p_k$ is the $k$th prime. Is it true that$$\underset{n}{\mathrm{limsup}}(f(n)-2p_n)=\infty ?$$

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

This question is *exactly* a conjecture of Carl Pomerance from his work on the “prime number graph,” and as far as the published literature I can locate goes, it is still **open**.

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.