Primality proof for n = 17321:

Take b = 2.

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

433 is prime.
b^((n-1)/433)-1 mod n = 9645, which is a unit, inverse 6149.

(433) divides n-1.

(433)^2 > n.

n is prime by Pocklington's theorem.