Primality proof for n = 13043:
Take b = 2.
b^(n-1) mod n = 1.
6521 is prime. b^((n-1)/6521)-1 mod n = 3, which is a unit, inverse 4348.
(6521) divides n-1.
(6521)^2 > n.
n is prime by Pocklington's theorem.