Primality proof for n = 176039071423:
Take b = 2.
b^(n-1) mod n = 1.
196911713 is prime.
b^((n-1)/196911713)-1 mod n = 77119920111, which is a unit, inverse 17159239061.
(196911713) divides n-1.
(196911713)^2 > n.
n is prime by Pocklington's theorem.