Primality proof for n = 113344013:

Take b = 2.

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

28336003 is prime.
b^((n-1)/28336003)-1 mod n = 15, which is a unit, inverse 98231478.

(28336003) divides n-1.

(28336003)^2 > n.

n is prime by Pocklington's theorem.