Primality proof for n = 22111:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=67.html>67 is prime.</a>
<br>b^((n-1)/67)-1 mod n = 12682, which is a unit, inverse 21642.
<p><a href=3.html>3 is prime.</a>
<br>b^((n-1)/3)-1 mod n = 7857, which is a unit, inverse 19491.
<p>(3 * 67) divides n-1.
<p>(3 * 67)^2 > n.
<p>n is prime by Pocklington's theorem.