Primality proof for n = 76031689039:
Take b = 2.
b^(n-1) mod n = 1.
119611 is prime.
b^((n-1)/119611)-1 mod n = 42573396014, which is a unit, inverse 68677618170.
105943 is prime.
b^((n-1)/105943)-1 mod n = 40157199381, which is a unit, inverse 27813492411.
(105943 * 119611) divides n-1.
(105943 * 119611)^2 > n.
n is prime by Pocklington's theorem.