Primality proof for n = 1013:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=23.html>23 is prime.</a>
<br>b^((n-1)/23)-1 mod n = 252, which is a unit, inverse 607.
<p><a href=2.html>2 is prime.</a>
<br>b^((n-1)/2)-1 mod n = 1011, which is a unit, inverse 506.
<p>(2^2 * 23) divides n-1.
<p>(2^2 * 23)^2 > n.
<p>n is prime by Pocklington's theorem.