Primality proof for n = 58309:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=113.html>113 is prime.</a>
<br>b^((n-1)/113)-1 mod n = 2027, which is a unit, inverse 24480.
<p><a href=2.html>2 is prime.</a>
<br>b^((n-1)/2)-1 mod n = 58307, which is a unit, inverse 29154.
<p>(2^2 * 113) divides n-1.
<p>(2^2 * 113)^2 > n.
<p>n is prime by Pocklington's theorem.