Primality proof for n = 1471:

Take b = 2.

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

7 is prime.
b^((n-1)/7)-1 mod n = 665, which is a unit, inverse 772.

(7^2) divides n-1.

(7^2)^2 > n.

n is prime by Pocklington's theorem.