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.