Primality proof for n = 2593:

Take b = 2.

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

3 is prime.
b^((n-1)/3)-1 mod n = 1136, which is a unit, inverse 1349.

(3^4) divides n-1.

(3^4)^2 > n.

n is prime by Pocklington's theorem.