Primality proof for n = 409:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=17.html>17 is prime.</a>
<br>b^((n-1)/17)-1 mod n = 35, which is a unit, inverse 187.
<p><a href=3.html>3 is prime.</a>
<br>b^((n-1)/3)-1 mod n = 354, which is a unit, inverse 290.
<p>(3 * 17) divides n-1.
<p>(3 * 17)^2 > n.
<p>n is prime by Pocklington's theorem.