Primality proof for n = 53448597593:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=513928823.html>513928823 is prime.</a>
<br>b^((n-1)/513928823)-1 mod n = 45025957920, which is a unit, inverse 45748318180.
<p>(513928823) divides n-1.
<p>(513928823)^2 > n.
<p>n is prime by Pocklington's theorem.