What are the least sets of generators for $S_n$

I think $(1,2), (1,2,\ldots, n)$ is also a set of generators.

It is proved in

J. D. Dixon, The probability of generating the symmetric group, Math. Z. 110 (1969), 199–205.

that the probability that a random pair elements of $S_n$ generate $S_n$ approaches $3/4$ has $n \to \infty$, and the probability that they generate $A_n$ approaches $1/4$.