Primality proof for n = 324256523:
Take b = 2.
b^(n-1) mod n = 1.
162128261 is prime. b^((n-1)/162128261)-1 mod n = 3, which is a unit, inverse 108085508.
(162128261) divides n-1.
(162128261)^2 > n.
n is prime by Pocklington's theorem.