Primality proof for n = 323757349:

Take b = 2.

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

26979779 is prime.
b^((n-1)/26979779)-1 mod n = 4095, which is a unit, inverse 188245726.

(26979779) divides n-1.

(26979779)^2 > n.

n is prime by Pocklington's theorem.