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.