Problem 891

Erdős Problem #891: declared status 'open'. Formalized: yes. Let $2=p_1<p_2<\cdots$ be the primes and $k\geq 2$. Is it true that, for all sufficiently large $n$, there must exist an integer in $[n,n+p_1\cdots p_k)$ with $>k$ many prime factors? Current best: By Dickson's conjecture there are infinitely many $n'$ such that $\frac{L_k}{m}n'+1$ is prime for all $1\leq m<p_1\cdots p_k$. Prize: no. Tags: number theory.