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.