Primality proof for n = 308713:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=677.html>677 is prime.</a>
<br>b^((n-1)/677)-1 mod n = 165419, which is a unit, inverse 264356.
<p>(677) divides n-1.
<p>(677)^2 > n.
<p>n is prime by Pocklington's theorem.