Primality proof for n = 671165898617413417:

Take b = 3.

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

1325514287 is prime.
b^((n-1)/1325514287)-1 mod n = 360058255460107342, which is a unit, inverse 633624280482534409.

(1325514287) divides n-1.

(1325514287)^2 > n.

n is prime by Pocklington's theorem.