Primality proof for n = 1137346319589436823:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=5842037431.html>5842037431 is prime.</a>
<br>b^((n-1)/5842037431)-1 mod n = 43895638642786331, which is a unit, inverse 296884222298623773.
<p>(5842037431) divides n-1.
<p>(5842037431)^2 > n.
<p>n is prime by Pocklington's theorem.