Primality proof for n = 250681:

Take b = 2.

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

2089 is prime.
b^((n-1)/2089)-1 mod n = 157963, which is a unit, inverse 148549.

(2089) divides n-1.

(2089)^2 > n.

n is prime by Pocklington's theorem.