Primality proof for n = 108763483:
Take b = 2.
b^(n-1) mod n = 1.
18127247 is prime. b^((n-1)/18127247)-1 mod n = 63, which is a unit, inverse 3452809.
(18127247) divides n-1.
(18127247)^2 > n.
n is prime by Pocklington's theorem.