Primality proof for n = 115347420731:

Take b = 2.

b^(n-1) mod n = 1.

11534742073 is prime.
b^((n-1)/11534742073)-1 mod n = 1023, which is a unit, inverse 95164440955.

(11534742073) divides n-1.

(11534742073)^2 > n.

n is prime by Pocklington's theorem.