Primality proof for n = 118277:

Take b = 2.

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

29569 is prime.
b^((n-1)/29569)-1 mod n = 15, which is a unit, inverse 55196.

(29569) divides n-1.

(29569)^2 > n.

n is prime by Pocklington's theorem.