Primality proof for n = 14875631:

Take b = 2.

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

19319 is prime.
b^((n-1)/19319)-1 mod n = 12219149, which is a unit, inverse 11839061.

(19319) divides n-1.

(19319)^2 > n.

n is prime by Pocklington's theorem.