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.