OPEN
This is open, and cannot be resolved with a finite computation.
Is there a function $f$ with $f(n)\to \infty$ as $n\to \infty$ such that, for all large $n$, there is a composite number $m$ such that\[n+f(n)<m<n+p(m)?\](Here $p(m)$ is the least prime factor of $m$.)
In
[Er92e] Erdős asks about\[F(n)=\min_{m>n}(m-p(m)),\]and whether $n-F(n)\sim cn^{1/2}$ for some $c>0$.
See also
[385].
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When referring to this problem, please use the original sources of Erdős. If you wish to acknowledge this website, the recommended citation format is:
T. F. Bloom, Erdős Problem #463, https://www.erdosproblems.com/463, accessed 2026-01-16
