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.