Primality proof for n = 11616307:
Take b = 2.
b^(n-1) mod n = 1.
148927 is prime. b^((n-1)/148927)-1 mod n = 8096884, which is a unit, inverse 1896036.
(148927) divides n-1.
(148927)^2 > n.
n is prime by Pocklington's theorem.