Primality proof for n = 1130119423:
Take b = 2.
b^(n-1) mod n = 1.
188353237 is prime. b^((n-1)/188353237)-1 mod n = 63, which is a unit, inverse 896920177.
(188353237) divides n-1.
(188353237)^2 > n.
n is prime by Pocklington's theorem.