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.