In
[Va99] it is asked whether $968$ is the largest integer with this property, but this is an error, since for example $968-9=7\cdot 137$.
The list of $n$ satisfying the given property is
A214583 in the OEIS. The largest known such $n$ is $1722$.
ChatGPT and Tang
have shown that the number of such $n$ in $[1,N]$ is at most $N^{1/2+o(1)}$.
An internal OpenAI model (see
[APSSV26b]) has resolved this, proving that for any integer $a\geq 1$ there are only finitely many $n$ such that $n-ak^2$ is prime for all $k$ with $(k,n)=1$ and $ak^2<n$, deducing this from a result of Pollack
[Po17].
See also
[1140] and
[1142].
View the LaTeX source
This page was last edited 09 April 2026. View history
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 #1141, https://www.erdosproblems.com/1141, accessed 2026-04-11
