The uniform prime-order conjugacy-class generation conjecture for finite simple groups of Lie type

Let $G$ be a finite simple group of Lie type. A conjugacy class consists of elements of prime order if every element in it has prime order.

Prime-order generation conjecture. With finitely many exceptions, there exist conjugacy classes $C$ and $D$ of $G$ consisting of elements of prime order such that

$$\langle x,y\rangle=G$$

for every $(x,y)\in C\times D$.

This strengthens the preceding generation result by requiring both classes to consist of prime-order elements and requiring every such pair to generate the whole group. The examples discussed immediately before the conjecture show that the assertion cannot hold without finitely many exceptions.