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.