Primality proof for n = 8191:
<p>Take b = 3.
<p>b^(n-1) mod n = 1.
<p><a href=13.html>13 is prime.</a>
<br>b^((n-1)/13)-1 mod n = 4095, which is a unit, inverse 8189.
<p><a href=7.html>7 is prime.</a>
<br>b^((n-1)/7)-1 mod n = 6762, which is a unit, inverse 5646.
<p>(7 * 13) divides n-1.
<p>(7 * 13)^2 > n.
<p>n is prime by Pocklington's theorem.