Primality proof for n = 2039:
Take b = 2.
b^(n-1) mod n = 1.
1019 is prime. b^((n-1)/1019)-1 mod n = 3, which is a unit, inverse 680.
(1019) divides n-1.
(1019)^2 > n.
n is prime by Pocklington's theorem.