Primality proof for n = 2269:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=7.html>7 is prime.</a>
<br>b^((n-1)/7)-1 mod n = 737, which is a unit, inverse 665.
<p><a href=3.html>3 is prime.</a>
<br>b^((n-1)/3)-1 mod n = 2185, which is a unit, inverse 27.
<p>(3^4 * 7) divides n-1.
<p>(3^4 * 7)^2 > n.
<p>n is prime by Pocklington's theorem.