Problem 663

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Statement. 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

$$q(n,k)<(1+o(1))\log n?$$

Status. Open.

Source. erdosproblems.com/663, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #663, https://www.erdosproblems.com/663.

Formalization. None recorded.

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