Primality proof for n = 6051631:
Take b = 2.
b^(n-1) mod n = 1.
263 is prime.
b^((n-1)/263)-1 mod n = 3483354, which is a unit, inverse 865403.
59 is prime.
b^((n-1)/59)-1 mod n = 5588904, which is a unit, inverse 2321130.
(59 * 263) divides n-1.
(59 * 263)^2 > n.
n is prime by Pocklington's theorem.