Primality proof for n = 313:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=13.html>13 is prime.</a>
<br>b^((n-1)/13)-1 mod n = 102, which is a unit, inverse 89.
<p><a href=3.html>3 is prime.</a>
<br>b^((n-1)/3)-1 mod n = 213, which is a unit, inverse 241.
<p>(3 * 13) divides n-1.
<p>(3 * 13)^2 > n.
<p>n is prime by Pocklington's theorem.