Primality proof for n = 23580350111:
Take b = 2.
b^(n-1) mod n = 1.
3736981 is prime. b^((n-1)/3736981)-1 mod n = 8915777965, which is a unit, inverse 12360420495.
(3736981) divides n-1.
(3736981)^2 > n.
n is prime by Pocklington's theorem.