Primality proof for n = 16018527589:

Take b = 2.

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

2413883 is prime.
b^((n-1)/2413883)-1 mod n = 13992678812, which is a unit, inverse 11760072769.

(2413883) divides n-1.

(2413883)^2 > n.

n is prime by Pocklington's theorem.