Primality proof for n = 1999:
<p>Take b = 3.
<p>b^(n-1) mod n = 1.
<p><a href=37.html>37 is prime.</a>
<br>b^((n-1)/37)-1 mod n = 1308, which is a unit, inverse 81.
<p><a href=3.html>3 is prime.</a>
<br>b^((n-1)/3)-1 mod n = 807, which is a unit, inverse 1729.
<p>(3^3 * 37) divides n-1.
<p>(3^3 * 37)^2 > n.
<p>n is prime by Pocklington's theorem.