Primality proof for n = 324328607518902137:

Take b = 2.

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

309473862136357 is prime.
b^((n-1)/309473862136357)-1 mod n = 122830832121771286, which is a unit, inverse 34619925550435414.

(309473862136357) divides n-1.

(309473862136357)^2 > n.

n is prime by Pocklington's theorem.