Primality proof for n = 168650669431260323389:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=12695774573265607.html>12695774573265607 is prime.</a>
<br>b^((n-1)/12695774573265607)-1 mod n = 498220274880388418, which is a unit, inverse 132237738639215230653.
<p>(12695774573265607) divides n-1.
<p>(12695774573265607)^2 > n.
<p>n is prime by Pocklington's theorem.