Primality proof for n = 168631:
Take b = 2.
b^(n-1) mod n = 1.
73 is prime.
b^((n-1)/73)-1 mod n = 12699, which is a unit, inverse 42015.
11 is prime.
b^((n-1)/11)-1 mod n = 50854, which is a unit, inverse 116328.
(11 * 73) divides n-1.
(11 * 73)^2 > n.
n is prime by Pocklington's theorem.