Primality proof for n = 691:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=23.html>23 is prime.</a>
<br>b^((n-1)/23)-1 mod n = 378, which is a unit, inverse 404.
<p><a href=5.html>5 is prime.</a>
<br>b^((n-1)/5)-1 mod n = 131, which is a unit, inverse 211.
<p>(5 * 23) divides n-1.
<p>(5 * 23)^2 > n.
<p>n is prime by Pocklington's theorem.