Primality proof for n = 3499:
Take b = 2.
b^(n-1) mod n = 1.
53 is prime.
b^((n-1)/53)-1 mod n = 1794, which is a unit, inverse 747.
11 is prime.
b^((n-1)/11)-1 mod n = 222, which is a unit, inverse 2443.
(11 * 53) divides n-1.
(11 * 53)^2 > n.
n is prime by Pocklington's theorem.