Primality proof for n = 256901:

Take b = 2.

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

367 is prime.
b^((n-1)/367)-1 mod n = 112649, which is a unit, inverse 41084.

5 is prime.
b^((n-1)/5)-1 mod n = 191062, which is a unit, inverse 231191.

(5^2 * 367) divides n-1.

(5^2 * 367)^2 > n.

n is prime by Pocklington's theorem.