Primality proof for n = 2089:
<p>Take b = 3.
<p>b^(n-1) mod n = 1.
<p><a href=29.html>29 is prime.</a>
<br>b^((n-1)/29)-1 mod n = 31, which is a unit, inverse 1213.
<p><a href=3.html>3 is prime.</a>
<br>b^((n-1)/3)-1 mod n = 825, which is a unit, inverse 1813.
<p>(3^2 * 29) divides n-1.
<p>(3^2 * 29)^2 > n.
<p>n is prime by Pocklington's theorem.