Primality proof for n = 57660685428664091:

Take b = 2.

b^(n-1) mod n = 1.

757986407 is prime.
b^((n-1)/757986407)-1 mod n = 2694799310712198, which is a unit, inverse 28666511356537955.

(757986407) divides n-1.

(757986407)^2 > n.

n is prime by Pocklington's theorem.