Primality proof for n = 569:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=71.html>71 is prime.</a>
<br>b^((n-1)/71)-1 mod n = 255, which is a unit, inverse 270.
<p>(71) divides n-1.
<p>(71)^2 > n.
<p>n is prime by Pocklington's theorem.