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.