Primality proof for n = 12569:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=1571.html>1571 is prime.</a>
<br>b^((n-1)/1571)-1 mod n = 255, which is a unit, inverse 1528.
<p>(1571) divides n-1.
<p>(1571)^2 > n.
<p>n is prime by Pocklington's theorem.