Primality proof for n = 13943143:
Take b = 2.
b^(n-1) mod n = 1.
26711 is prime. b^((n-1)/26711)-1 mod n = 6309612, which is a unit, inverse 2025555.
(26711) divides n-1.
(26711)^2 > n.
n is prime by Pocklington's theorem.