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.