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.