Primality proof for n = 1001447:

Take b = 2.

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

500723 is prime.
b^((n-1)/500723)-1 mod n = 3, which is a unit, inverse 333816.

(500723) divides n-1.

(500723)^2 > n.

n is prime by Pocklington's theorem.