Primality proof for n = 124471:

Take b = 2.

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

461 is prime.
b^((n-1)/461)-1 mod n = 26527, which is a unit, inverse 25934.

(461) divides n-1.

(461)^2 > n.

n is prime by Pocklington's theorem.