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.