Primality proof for n = 116961023:

Take b = 2.

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

58480511 is prime.
b^((n-1)/58480511)-1 mod n = 3, which is a unit, inverse 38987008.

(58480511) divides n-1.

(58480511)^2 > n.

n is prime by Pocklington's theorem.