Primality proof for n = 17171153:

Take b = 2.

b^(n-1) mod n = 1.

20249 is prime.
b^((n-1)/20249)-1 mod n = 11619796, which is a unit, inverse 13961520.

(20249) divides n-1.

(20249)^2 > n.

n is prime by Pocklington's theorem.