Primality proof for n = 193:
<p>Take b = 5.
<p>b^(n-1) mod n = 1.
<p><a href=3.html>3 is prime.</a>
<br>b^((n-1)/3)-1 mod n = 83, which is a unit, inverse 100.
<p><a href=2.html>2 is prime.</a>
<br>b^((n-1)/2)-1 mod n = 191, which is a unit, inverse 96.
<p>(2^6 * 3) divides n-1.
<p>(2^6 * 3)^2 > n.
<p>n is prime by Pocklington's theorem.