Primality proof for n = 157427:

Take b = 2.

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

78713 is prime.
b^((n-1)/78713)-1 mod n = 3, which is a unit, inverse 52476.

(78713) divides n-1.

(78713)^2 > n.

n is prime by Pocklington's theorem.