Problem 451

Erdős Problem #451: declared status 'open'. Formalized: no. Estimate $n_k$, the smallest integer $>2k$ such that $\prod_{1\leq i\leq k}(n_k-i)$ has no prime factor in $(k,2k)$. Current best: Adenwalla observes that an easy upper bound is $n_k\leq \prod_{k<p<2k}p=e^{O(k)}$. Prize: no. OEIS: A386620. Tags: number theory.