Primality proof for n = 6700417:

Take b = 3.

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

17449 is prime.
b^((n-1)/17449)-1 mod n = 5846539, which is a unit, inverse 4499094.

(17449) divides n-1.

(17449)^2 > n.

n is prime by Pocklington's theorem.