Primality proof for n = 116359:
Take b = 2.
b^(n-1) mod n = 1.
43 is prime.
b^((n-1)/43)-1 mod n = 70258, which is a unit, inverse 30654.
11 is prime.
b^((n-1)/11)-1 mod n = 43890, which is a unit, inverse 60714.
(11 * 43) divides n-1.
(11 * 43)^2 > n.
n is prime by Pocklington's theorem.