Primality proof for n = 31:
<p>Take b = 3.
<p>b^(n-1) mod n = 1.
<p><a href=5.html>5 is prime.</a>
<br>b^((n-1)/5)-1 mod n = 15, which is a unit, inverse 29.
<p><a href=3.html>3 is prime.</a>
<br>b^((n-1)/3)-1 mod n = 24, which is a unit, inverse 22.
<p>(3 * 5) divides n-1.
<p>(3 * 5)^2 > n.
<p>n is prime by Pocklington's theorem.