Primality proof for n = 256117:
Take b = 2.
b^(n-1) mod n = 1.
3049 is prime. b^((n-1)/3049)-1 mod n = 240561, which is a unit, inverse 211285.
(3049) divides n-1.
(3049)^2 > n.
n is prime by Pocklington's theorem.