Primality proof for n = 114691:

Take b = 2.

b^(n-1) mod n = 1.

3823 is prime.
b^((n-1)/3823)-1 mod n = 4681, which is a unit, inverse 17641.

(3823) divides n-1.

(3823)^2 > n.

n is prime by Pocklington's theorem.