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.