Problem 860

Erdős Problem #860: declared status 'open'. Formalized: no. Let $h(n)$ be such that, for any $m\geq 1$, in the interval $(m,m+h(n))$ there exist distinct integers $a_i$ for $1\leq i\leq \pi(n)$ such that $p_i\mid a_i$, where $p_i$ denotes the $i$th prime. Estimate $h(n)$. Prize: no. OEIS: A048670, A058989. Tags: number theory, primes.