Primality proof for n = 1693:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=47.html>47 is prime.</a>
<br>b^((n-1)/47)-1 mod n = 641, which is a unit, inverse 1244.
<p>(47) divides n-1.
<p>(47)^2 > n.
<p>n is prime by Pocklington's theorem.