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.