Primality proof for n = 13331831:

Take b = 2.

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

1373 is prime.
b^((n-1)/1373)-1 mod n = 1207233, which is a unit, inverse 1512291.

971 is prime.
b^((n-1)/971)-1 mod n = 2792113, which is a unit, inverse 10572798.

(971 * 1373) divides n-1.

(971 * 1373)^2 > n.

n is prime by Pocklington's theorem.