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.