Primality proof for n = 52934372406331568616067:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=1137346319589436823.html>1137346319589436823 is prime.</a>
<br>b^((n-1)/1137346319589436823)-1 mod n = 38013909046553348206565, which is a unit, inverse 17208243580045568319523.
<p>(1137346319589436823) divides n-1.
<p>(1137346319589436823)^2 > n.
<p>n is prime by Pocklington's theorem.