Primality proof for n = 71:

Take b = 2.

b^(n-1) mod n = 1.

7 is prime.
b^((n-1)/7)-1 mod n = 29, which is a unit, inverse 49.

5 is prime.
b^((n-1)/5)-1 mod n = 53, which is a unit, inverse 67.

(5 * 7) divides n-1.

(5 * 7)^2 > n.

n is prime by Pocklington's theorem.