Primality proof for n = 1993:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=83.html>83 is prime.</a>
<br>b^((n-1)/83)-1 mod n = 141, which is a unit, inverse 1258.
<p>(83) divides n-1.
<p>(83)^2 > n.
<p>n is prime by Pocklington's theorem.