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.