Primality proof for n = 802330687:
Take b = 2.
b^(n-1) mod n = 1.
44573927 is prime. b^((n-1)/44573927)-1 mod n = 262143, which is a unit, inverse 463622709.
(44573927) divides n-1.
(44573927)^2 > n.
n is prime by Pocklington's theorem.