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.