Primality proof for n = 1562647:
Take b = 2.
b^(n-1) mod n = 1.
260441 is prime. b^((n-1)/260441)-1 mod n = 63, which is a unit, inverse 942549.
(260441) divides n-1.
(260441)^2 > n.
n is prime by Pocklington's theorem.