OPEN
Let $p_k$ denote the $k$th prime. For infinitely many $r$ there are at least two integers $p_r<n<p_{r+1}$ all of whose prime factors are $<p_{r+1}-p_r$.
Erdős thought this was true but that there are very few such $r$. He could show that the density of $r$ such that at least one such $n$ exist is $0$.
