Primality proof for n = 670261:

Take b = 2.

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

11171 is prime.
b^((n-1)/11171)-1 mod n = 201447, which is a unit, inverse 647719.

(11171) divides n-1.

(11171)^2 > n.

n is prime by Pocklington's theorem.