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.