Erdős Problem #393

The problem

Let $f(n)$ denote the minimal $m\geq 1$ such that

$$n! = a_1\cdots a_t$$

with $a_1<\cdots <a_t=a_1+m$. What is the behaviour of $f(n)$?

Statement quoted from erdosproblems.com/393, maintained by Thomas Bloom. Original source: [ErGr80,p.76]. Current status there: open.

AI contributions

As recorded in Terence Tao's wiki AI contributions to Erdős problems (data as of 30 Jun 2026). 🟢 full, 🟡 partial, ⚪ unverified, 🔴 incorrect.

Caveats

The wiki's classifications are provisional and are not a benchmark. Many Erdős problems have never had a thorough literature review, so a result that looks new may later turn out to be known; some problems were also stated ambiguously or incorrectly. See the problem page for the full discussion.

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