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.