Primality proof for n = 29569:
<p>Take b = 3.
<p>b^(n-1) mod n = 1.
<p><a href=11.html>11 is prime.</a>
<br>b^((n-1)/11)-1 mod n = 9117, which is a unit, inverse 13638.
<p><a href=7.html>7 is prime.</a>
<br>b^((n-1)/7)-1 mod n = 3701, which is a unit, inverse 7582.
<p><a href=3.html>3 is prime.</a>
<br>b^((n-1)/3)-1 mod n = 16509, which is a unit, inverse 24065.
<p>(3 * 7 * 11) divides n-1.
<p>(3 * 7 * 11)^2 > n.
<p>n is prime by Pocklington's theorem.