Almost All Alternating Groups are Invariably Generated by Two Elements of Prime Order

We show that for all n≤X apart from O(Xexp(−c(logX)1/2(loglogX)1/2)) exceptions, the alternating group An is invariably generated by two elements of prime order. This answers (in a quantitative form) a question of Guralnick, Shareshian, and Woodroofe.