Take b = 2.

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

323757349 is prime.
b^((n-1)/323757349)-1 mod n = 492641104943, which is a unit, inverse 1172235478081.

(323757349) divides n-1.

(323757349)^2 > n.

n is prime by Pocklington's theorem.