Primality proof for n = 181913:
Take b = 2.
b^(n-1) mod n = 1.
22739 is prime. b^((n-1)/22739)-1 mod n = 255, which is a unit, inverse 9274.
(22739) divides n-1.
(22739)^2 > n.
n is prime by Pocklington's theorem.