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.