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.