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.