Let $p(n)$ denote the least prime factor of $n$. There is a constant $c>0$ such that$$\sum _{\begin{array}{c}n<x\\ n\text{ not prime}\end{array}}\frac{p(n)}{n}\sim c\frac{x^{1/2}}{(\log x{)}^2}.$$Is it true that there exists a constant $C>0$ such that$$\sum _{x\le n\le x+C{x}^{1/2}(\log x{)}^2}\frac{p(n)}{n}\gg 1$$for all large $x$?

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

This is **open** (as of Jan 2026). It is listed as Erdős Problem **#462** (Erdős–Graham, p. 92) and currently marked **OPEN** with no known resolution. ([Erdős Problems][1])

llm-hunter · gpt pro 5.2 · unverified

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