Primality proof for n = 2413883:

Take b = 2.

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

1206941 is prime.
b^((n-1)/1206941)-1 mod n = 3, which is a unit, inverse 804628.

(1206941) divides n-1.

(1206941)^2 > n.

n is prime by Pocklington's theorem.