Primality proof for n = 173297:
Take b = 2.
b^(n-1) mod n = 1.
10831 is prime. b^((n-1)/10831)-1 mod n = 65535, which is a unit, inverse 99935.
(10831) divides n-1.
(10831)^2 > n.
n is prime by Pocklington's theorem.