Primality proof for n = 123606883:

Take b = 2.

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

337 is prime.
b^((n-1)/337)-1 mod n = 51511412, which is a unit, inverse 75742957.

71 is prime.
b^((n-1)/71)-1 mod n = 16774174, which is a unit, inverse 28589215.

(71 * 337) divides n-1.

(71 * 337)^2 > n.

n is prime by Pocklington's theorem.