Primality proof for n = 122232809:
Take b = 2.
b^(n-1) mod n = 1.
372661 is prime. b^((n-1)/372661)-1 mod n = 565082, which is a unit, inverse 39762295.
(372661) divides n-1.
(372661)^2 > n.
n is prime by Pocklington's theorem.