Grimm's Conjecture

Conjecture
Let $n$ and $k$ be positive integers.

Let $n+1, n+2, \dots, n+k$ be composite numbers.

Then there exists a finite sequence $\left\langle{p_i}\right\rangle$ of $k$ distinct primes such that $p_i$ divides $n+i$ for each natural number $i$ such that $1 \le i \le k$.