Primality proof for n = 31327:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=227.html>227 is prime.</a>
<br>b^((n-1)/227)-1 mod n = 17439, which is a unit, inverse 25478.
<p>(227) divides n-1.
<p>(227)^2 > n.
<p>n is prime by Pocklington's theorem.