Primality proof for n = 311245691:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=311.html>311 is prime.</a>
<br>b^((n-1)/311)-1 mod n = 123550162, which is a unit, inverse 89454809.
<p><a href=29.html>29 is prime.</a>
<br>b^((n-1)/29)-1 mod n = 120750128, which is a unit, inverse 134145418.
<p>(29^2 * 311) divides n-1.
<p>(29^2 * 311)^2 > n.
<p>n is prime by Pocklington's theorem.