Primality proof for n = 71429:
Take b = 2.
b^(n-1) mod n = 1.
2551 is prime. b^((n-1)/2551)-1 mod n = 5273, which is a unit, inverse 62922.
(2551) divides n-1.
(2551)^2 > n.
n is prime by Pocklington's theorem.