Primality proof for n = 1093:
Take b = 2.
b^(n-1) mod n = 1.
13 is prime.
b^((n-1)/13)-1 mod n = 900, which is a unit, inverse 538.
7 is prime.
b^((n-1)/7)-1 mod n = 8, which is a unit, inverse 410.
(7 * 13) divides n-1.
(7 * 13)^2 > n.
n is prime by Pocklington's theorem.