Primality proof for n = 8039:
Take b = 2.
b^(n-1) mod n = 1.
4019 is prime. b^((n-1)/4019)-1 mod n = 3, which is a unit, inverse 2680.
(4019) divides n-1.
(4019)^2 > n.
n is prime by Pocklington's theorem.