Primality proof for n = 24821:

Take b = 2.

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

73 is prime.
b^((n-1)/73)-1 mod n = 9049, which is a unit, inverse 7203.

17 is prime.
b^((n-1)/17)-1 mod n = 11546, which is a unit, inverse 22682.

(17 * 73) divides n-1.

(17 * 73)^2 > n.

n is prime by Pocklington's theorem.