Are there infinitely many primes $p$ such that every even number $n\le p-3$ can be written as a difference of primes $n=q_1-q_2$ where $q_1,q_2\le p$?

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

This is an **open problem** (asked by Erdős). Primes $p$ with your property are called **cluster primes**: an odd prime $p$ such that every even (k\le p-3) can be written as (k=q_1-q_2) with primes (q_1,q_2\le p). ([Wikipedia][1])

llm-hunter · gpt 5.2, gpt pro 5.2 · unverified

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