Primality proof for n = 16693:
Take b = 2.
b^(n-1) mod n = 1.
107 is prime.
b^((n-1)/107)-1 mod n = 3503, which is a unit, inverse 15373.
13 is prime.
b^((n-1)/13)-1 mod n = 4955, which is a unit, inverse 2840.
(13 * 107) divides n-1.
(13 * 107)^2 > n.
n is prime by Pocklington's theorem.