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.