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.