Primality proof for n = 68632771:
Take b = 2.
b^(n-1) mod n = 1.
55799 is prime. b^((n-1)/55799)-1 mod n = 44113422, which is a unit, inverse 27045022.
(55799) divides n-1.
(55799)^2 > n.
n is prime by Pocklington's theorem.