Primality proof for n = 1002328039319:

Take b = 2.

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

3969899 is prime.
b^((n-1)/3969899)-1 mod n = 221842812586, which is a unit, inverse 718861591819.

(3969899) divides n-1.

(3969899)^2 > n.

n is prime by Pocklington's theorem.