Primality proof for n = 20593:
Take b = 5.
b^(n-1) mod n = 1.
13 is prime.
b^((n-1)/13)-1 mod n = 13172, which is a unit, inverse 1862.
11 is prime.
b^((n-1)/11)-1 mod n = 20039, which is a unit, inverse 1301.
3 is prime.
b^((n-1)/3)-1 mod n = 142, which is a unit, inverse 6816.
(3^2 * 11 * 13) divides n-1.
(3^2 * 11 * 13)^2 > n.
n is prime by Pocklington's theorem.