Primality proof for n = 17231:
Take b = 2.
b^(n-1) mod n = 1.
1723 is prime. b^((n-1)/1723)-1 mod n = 1023, which is a unit, inverse 3554.
(1723) divides n-1.
(1723)^2 > n.
n is prime by Pocklington's theorem.