Primality proof for n = 250259:

Take b = 2.

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

797 is prime.
b^((n-1)/797)-1 mod n = 45917, which is a unit, inverse 103631.

(797) divides n-1.

(797)^2 > n.

n is prime by Pocklington's theorem.