Primality proof for n = 80629:
Take b = 2.
b^(n-1) mod n = 1.
6719 is prime. b^((n-1)/6719)-1 mod n = 4095, which is a unit, inverse 20300.
(6719) divides n-1.
(6719)^2 > n.
n is prime by Pocklington's theorem.