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.