Primality proof for n = 24709:

Take b = 2.

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

71 is prime.
b^((n-1)/71)-1 mod n = 18360, which is a unit, inverse 15034.

29 is prime.
b^((n-1)/29)-1 mod n = 6264, which is a unit, inverse 15096.

(29 * 71) divides n-1.

(29 * 71)^2 > n.

n is prime by Pocklington's theorem.