Primality proof for n = 1409:
<p>Take b = 3.
<p>b^(n-1) mod n = 1.
<p><a href=11.html>11 is prime.</a>
<br>b^((n-1)/11)-1 mod n = 991, which is a unit, inverse 300.
<p><a href=2.html>2 is prime.</a>
<br>b^((n-1)/2)-1 mod n = 1407, which is a unit, inverse 704.
<p>(2^7 * 11) divides n-1.
<p>(2^7 * 11)^2 > n.
<p>n is prime by Pocklington's theorem.