Primality proof for n = 1569301:

Take b = 2.

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

5231 is prime.
b^((n-1)/5231)-1 mod n = 1494009, which is a unit, inverse 635228.

(5231) divides n-1.

(5231)^2 > n.

n is prime by Pocklington's theorem.