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.