Problem 663

Erdős Problem #663: declared status 'open'. Formalized: no. Let $k\geq 2$ and $q(n,k)$ denote the least prime which does not divide $\prod_{1\leq i\leq k}(n+i)$. Is it true that, if $k$ is fixed and $n$ is sufficiently large, we have$$q(n,k)<(1+o(1))\log n?$$ Prize: no. OEIS: A391668. Tags: number theory.