Primality proof for n = 11799461:
Take b = 2.
b^(n-1) mod n = 1.
227 is prime.
b^((n-1)/227)-1 mod n = 10183703, which is a unit, inverse 317399.
113 is prime.
b^((n-1)/113)-1 mod n = 1872389, which is a unit, inverse 4199685.
(113 * 227) divides n-1.
(113 * 227)^2 > n.
n is prime by Pocklington's theorem.