Primality proof for n = 2657:

Take b = 2.

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

83 is prime.
b^((n-1)/83)-1 mod n = 1191, which is a unit, inverse 1314.

(83) divides n-1.

(83)^2 > n.

n is prime by Pocklington's theorem.