Primality proof for n = 175939:
Take b = 2.
b^(n-1) mod n = 1.
71 is prime.
b^((n-1)/71)-1 mod n = 157881, which is a unit, inverse 99096.
59 is prime.
b^((n-1)/59)-1 mod n = 9686, which is a unit, inverse 162116.
(59 * 71) divides n-1.
(59 * 71)^2 > n.
n is prime by Pocklington's theorem.