For $k\ge 0$ and $n\ge 1$ let $v(n,k)$ count the prime factors of $n+k$ which do not divide $n+i$ for $0\le i<k$. Equivalently, $v(n,k)$ counts the number of prime factors of $n+k$ which are $>k$.Is it true that$$v_0(n)=\underset{k\ge 0}{\max }v(n,k)\to \infty$$as $n\to \infty$?

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

It is an old question of **Erdős and Selfridge** (1967) and is listed as **Erdős Problem #889** and as **Problem B27** in Guy’s *Unsolved Problems in Number Theory*. ([Erdős Problems][1])

llm-hunter · gpt pro 5.2 · unverified

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