Primality proof for n = 3571:
Take b = 2.
b^(n-1) mod n = 1.
17 is prime.
b^((n-1)/17)-1 mod n = 1846, which is a unit, inverse 1151.
7 is prime.
b^((n-1)/7)-1 mod n = 2766, which is a unit, inverse 936.
(7 * 17) divides n-1.
(7 * 17)^2 > n.
n is prime by Pocklington's theorem.