Primality proof for n = 23311:
<p>Take b = 3.
<p>b^(n-1) mod n = 1.
<p><a href=37.html>37 is prime.</a>
<br>b^((n-1)/37)-1 mod n = 11310, which is a unit, inverse 14776.
<p><a href=7.html>7 is prime.</a>
<br>b^((n-1)/7)-1 mod n = 7031, which is a unit, inverse 3710.
<p>(7 * 37) divides n-1.
<p>(7 * 37)^2 > n.
<p>n is prime by Pocklington's theorem.