Primality proof for n = 116989:
Take b = 2.
b^(n-1) mod n = 1.
9749 is prime. b^((n-1)/9749)-1 mod n = 4095, which is a unit, inverse 24312.
(9749) divides n-1.
(9749)^2 > n.
n is prime by Pocklington's theorem.