Primality proof for n = 124769:

Take b = 2.

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

557 is prime.
b^((n-1)/557)-1 mod n = 91926, which is a unit, inverse 68913.

(557) divides n-1.

(557)^2 > n.

n is prime by Pocklington's theorem.