Primality proof for n = 122299:
Take b = 2.
b^(n-1) mod n = 1.
109 is prime.
b^((n-1)/109)-1 mod n = 45591, which is a unit, inverse 49506.
17 is prime.
b^((n-1)/17)-1 mod n = 68475, which is a unit, inverse 46796.
(17 * 109) divides n-1.
(17 * 109)^2 > n.
n is prime by Pocklington's theorem.