Primality proof for n = 3023:
Take b = 2.
b^(n-1) mod n = 1.
1511 is prime. b^((n-1)/1511)-1 mod n = 3, which is a unit, inverse 1008.
(1511) divides n-1.
(1511)^2 > n.
n is prime by Pocklington's theorem.