Problem Statement
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 $m$.)
Categories:
Number Theory Primes
Progress
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].
Source: erdosproblems.com/463 | Last verified: January 15, 2026