Primality proof for n = 8821:
<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 = 3693, which is a unit, inverse 8403.
<p><a href=5.html>5 is prime.</a>
<br>b^((n-1)/5)-1 mod n = 4911, which is a unit, inverse 5349.
<p>(5 * 7^2) divides n-1.
<p>(5 * 7^2)^2 > n.
<p>n is prime by Pocklington's theorem.