OPEN
Find some reasonable function $f(n)$ such that, for almost all integers $n$, the least integer $m$ such that $m\nmid \binom{2n}{n}$ satisfies
\[m\sim f(n).\]
A problem of Erdős, Graham, Ruzsa, and Straus
[EGRS75], who say it is 'not hard to show that', for almost all $n$, the minimal such $m$ satisfies
\[m=\exp((\log n)^{1/2+o(1)}).\]
