Primality proof for n = 683:
<p>Take b = 3.
<p>b^(n-1) mod n = 1.
<p><a href=31.html>31 is prime.</a>
<br>b^((n-1)/31)-1 mod n = 346, which is a unit, inverse 152.
<p>(31) divides n-1.
<p>(31)^2 > n.
<p>n is prime by Pocklington's theorem.