Primality proof for n = 17097494023:
Take b = 2.
b^(n-1) mod n = 1.
135694397 is prime.
b^((n-1)/135694397)-1 mod n = 9375292735, which is a unit, inverse 14249388548.
(135694397) divides n-1.
(135694397)^2 > n.
n is prime by Pocklington's theorem.