Primality proof for n = 29822497:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=911.html>911 is prime.</a>
<br>b^((n-1)/911)-1 mod n = 5342602, which is a unit, inverse 24573073.
<p><a href=31.html>31 is prime.</a>
<br>b^((n-1)/31)-1 mod n = 19185763, which is a unit, inverse 14921555.
<p>(31 * 911) divides n-1.
<p>(31 * 911)^2 > n.
<p>n is prime by Pocklington's theorem.