Primality proof for n = 24019:
Take b = 2.
b^(n-1) mod n = 1.
4003 is prime. b^((n-1)/4003)-1 mod n = 63, which is a unit, inverse 22494.
(4003) divides n-1.
(4003)^2 > n.
n is prime by Pocklington's theorem.