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.