Primality proof for n = 4093:

Take b = 2.

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

31 is prime.
b^((n-1)/31)-1 mod n = 1147, which is a unit, inverse 1877.

11 is prime.
b^((n-1)/11)-1 mod n = 99, which is a unit, inverse 1323.

(11 * 31) divides n-1.

(11 * 31)^2 > n.

n is prime by Pocklington's theorem.