Primality proof for n = 17299349:
Take b = 2.
b^(n-1) mod n = 1.
20693 is prime. b^((n-1)/20693)-1 mod n = 15338605, which is a unit, inverse 4102175.
(20693) divides n-1.
(20693)^2 > n.
n is prime by Pocklington's theorem.