Primality proof for n = 18413:
Take b = 2.
b^(n-1) mod n = 1.
4603 is prime. b^((n-1)/4603)-1 mod n = 15, which is a unit, inverse 15958.
(4603) divides n-1.
(4603)^2 > n.
n is prime by Pocklington's theorem.