Primality proof for n = 1583:
<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 = 553, which is a unit, inverse 979.
<p>(113) divides n-1.
<p>(113)^2 > n.
<p>n is prime by Pocklington's theorem.