Primality proof for n = 1293654617:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=63589.html>63589 is prime.</a>
<br>b^((n-1)/63589)-1 mod n = 205021467, which is a unit, inverse 495472994.
<p>(63589) divides n-1.
<p>(63589)^2 > n.
<p>n is prime by Pocklington's theorem.