Primality proof for n = 412771:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=13759.html>13759 is prime.</a>
<br>b^((n-1)/13759)-1 mod n = 124452, which is a unit, inverse 112453.
<p>(13759) divides n-1.
<p>(13759)^2 > n.
<p>n is prime by Pocklington's theorem.