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.