Primality proof for n = 31627:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=251.html>251 is prime.</a>
<br>b^((n-1)/251)-1 mod n = 8412, which is a unit, inverse 22081.
<p>(251) divides n-1.
<p>(251)^2 > n.
<p>n is prime by Pocklington's theorem.