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.