Primality proof for n = 3469:

Take b = 2.

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

17 is prime.
b^((n-1)/17)-1 mod n = 1094, which is a unit, inverse 371.

(17^2) divides n-1.

(17^2)^2 > n.

n is prime by Pocklington's theorem.