Primality proof for n = 24317:
Take b = 2.
b^(n-1) mod n = 1.
6079 is prime. b^((n-1)/6079)-1 mod n = 15, which is a unit, inverse 11348.
(6079) divides n-1.
(6079)^2 > n.
n is prime by Pocklington's theorem.