Primality proof for n = 17657:

Take b = 2.

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

2207 is prime.
b^((n-1)/2207)-1 mod n = 255, which is a unit, inverse 2562.

(2207) divides n-1.

(2207)^2 > n.

n is prime by Pocklington's theorem.