Primality proof for n = 16843:

Take b = 2.

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

401 is prime.
b^((n-1)/401)-1 mod n = 9926, which is a unit, inverse 13658.

(401) divides n-1.

(401)^2 > n.

n is prime by Pocklington's theorem.