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.