Primality proof for n = 408311:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=307.html>307 is prime.</a>
<br>b^((n-1)/307)-1 mod n = 128748, which is a unit, inverse 108503.
<p><a href=19.html>19 is prime.</a>
<br>b^((n-1)/19)-1 mod n = 266931, which is a unit, inverse 5288.
<p>(19 * 307) divides n-1.
<p>(19 * 307)^2 > n.
<p>n is prime by Pocklington's theorem.