Primality proof for n = 21682369618568459986649847415957985919370700162617:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=7545728982901378757453953508051.html>7545728982901378757453953508051 is prime.</a>
<br>b^((n-1)/7545728982901378757453953508051)-1 mod n = 12094932699534463020702203188591867047635730308051, which is a unit, inverse 11566037609640112930408334477136829464144005619644.
<p>(7545728982901378757453953508051) divides n-1.
<p>(7545728982901378757453953508051)^2 > n.
<p>n is prime by Pocklington's theorem.