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.