Primality proof for n = 118361:
Take b = 2.
b^(n-1) mod n = 1.
269 is prime.
b^((n-1)/269)-1 mod n = 77876, which is a unit, inverse 63006.
11 is prime.
b^((n-1)/11)-1 mod n = 98956, which is a unit, inverse 57311.
(11 * 269) divides n-1.
(11 * 269)^2 > n.
n is prime by Pocklington's theorem.