Primality proof for n = 15173:
Take b = 2.
b^(n-1) mod n = 1.
3793 is prime. b^((n-1)/3793)-1 mod n = 15, which is a unit, inverse 13150.
(3793) divides n-1.
(3793)^2 > n.
n is prime by Pocklington's theorem.