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.