Primality proof for n = 11716083324473119:
Take b = 2.
b^(n-1) mod n = 1.
22842497 is prime.
b^((n-1)/22842497)-1 mod n = 7325182935956143, which is a unit, inverse 6570772928389180.
2084989 is prime.
b^((n-1)/2084989)-1 mod n = 2360467097553465, which is a unit, inverse 4799401598133071.
(2084989 * 22842497) divides n-1.
(2084989 * 22842497)^2 > n.
n is prime by Pocklington's theorem.