Primality proof for n = 327923:

Take b = 2.

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

397 is prime.
b^((n-1)/397)-1 mod n = 37889, which is a unit, inverse 316464.

59 is prime.
b^((n-1)/59)-1 mod n = 139034, which is a unit, inverse 113719.

(59 * 397) divides n-1.

(59 * 397)^2 > n.

n is prime by Pocklington's theorem.