Primality proof for n = 122579:

Take b = 2.

b^(n-1) mod n = 1.

367 is prime.
b^((n-1)/367)-1 mod n = 75935, which is a unit, inverse 101006.

(367) divides n-1.

(367)^2 > n.

n is prime by Pocklington's theorem.