Generation of finite simple groups by two Sylow subgroups

Let $G$ be a finite simple group, and let $r$ and $s$ be primes dividing $|G|$. A Sylow-subgroup generation conjecture. There exist a Sylow $r$-subgroup $P$ and a Sylow $s$-subgroup $Q$ of $G$ such that

$$G=\langle P,Q\rangle.$$

This conjecture is the motivation for the paper's results on random generation by elements of prescribed prime orders and on generation by two Sylow subgroups. Its resolution status is not specified in the supplied text.