Primality proof for n = 29311:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=977.html>977 is prime.</a>
<br>b^((n-1)/977)-1 mod n = 21271, which is a unit, inverse 10175.
<p>(977) divides n-1.
<p>(977)^2 > n.
<p>n is prime by Pocklington's theorem.