Primality proof for n = 2423:

Take b = 2.

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

173 is prime.
b^((n-1)/173)-1 mod n = 1845, which is a unit, inverse 1790.

(173) divides n-1.

(173)^2 > n.

n is prime by Pocklington's theorem.