Primality proof for n = 323131:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=10771.html>10771 is prime.</a>
<br>b^((n-1)/10771)-1 mod n = 300641, which is a unit, inverse 34497.
<p>(10771) divides n-1.
<p>(10771)^2 > n.
<p>n is prime by Pocklington's theorem.