Primality proof for n = 2295569:

Take b = 2.

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

13043 is prime.
b^((n-1)/13043)-1 mod n = 493347, which is a unit, inverse 78148.

(13043) divides n-1.

(13043)^2 > n.

n is prime by Pocklington's theorem.