Primality proof for n = 331:

Take b = 2.

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

5 is prime.
b^((n-1)/5)-1 mod n = 63, which is a unit, inverse 310.

3 is prime.
b^((n-1)/3)-1 mod n = 298, which is a unit, inverse 10.

2 is prime.
b^((n-1)/2)-1 mod n = 329, which is a unit, inverse 165.

(2 * 3 * 5) divides n-1.

(2 * 3 * 5)^2 > n.

n is prime by Pocklington's theorem.