Primality proof for n = 3529:
Take b = 2.
b^(n-1) mod n = 1.
7 is prime.
b^((n-1)/7)-1 mod n = 2223, which is a unit, inverse 127.
3 is prime.
b^((n-1)/3)-1 mod n = 447, which is a unit, inverse 3379.
(3^2 * 7^2) divides n-1.
(3^2 * 7^2)^2 > n.
n is prime by Pocklington's theorem.