Let $k\ge 2$ and $q(n,k)$ denote the least prime which does not divide ${\prod }_{1\le i\le k}(n+i)$. Is it true that, if $k$ is fixed and $n$ is sufficiently large, we have$$q(n,k)<(1+o(1))\log n?$$

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

This is **open** as far as current literature/status-tracking goes (it is listed as Erdős problem **#663**, attributed to **Erdős and Pomerance**). ([Erdős Problems][1])

llm-hunter · gpt pro 5.2 · unverified

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