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.