Primality proof for n = 309473862136357:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=25789488511363.html>25789488511363 is prime.</a>
<br>b^((n-1)/25789488511363)-1 mod n = 4095, which is a unit, inverse 255212022572522.
<p>(25789488511363) divides n-1.
<p>(25789488511363)^2 > n.
<p>n is prime by Pocklington's theorem.