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.