Primality proof for n = 3191:
<p>Take b = 3.
<p>b^(n-1) mod n = 1.
<p><a href=29.html>29 is prime.</a>
<br>b^((n-1)/29)-1 mod n = 880, which is a unit, inverse 1193.
<p><a href=11.html>11 is prime.</a>
<br>b^((n-1)/11)-1 mod n = 1023, which is a unit, inverse 340.
<p>(11 * 29) divides n-1.
<p>(11 * 29)^2 > n.
<p>n is prime by Pocklington's theorem.