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.