Primality proof for n = 323116924469:

Take b = 2.

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

393203 is prime.
b^((n-1)/393203)-1 mod n = 83221253892, which is a unit, inverse 36351476685.

15803 is prime.
b^((n-1)/15803)-1 mod n = 58905450677, which is a unit, inverse 207820180676.

(15803 * 393203) divides n-1.

(15803 * 393203)^2 > n.

n is prime by Pocklington's theorem.