Primality proof for n = 6254681:

Take b = 2.

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

577 is prime.
b^((n-1)/577)-1 mod n = 1181281, which is a unit, inverse 2522536.

271 is prime.
b^((n-1)/271)-1 mod n = 280377, which is a unit, inverse 5133520.

(271 * 577) divides n-1.

(271 * 577)^2 > n.

n is prime by Pocklington's theorem.