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.