Primality proof for n = 186766509188519991823:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=294639853.html>294639853 is prime.</a>
<br>b^((n-1)/294639853)-1 mod n = 2877256809256278319, which is a unit, inverse 112338998508828700677.
<p><a href=285457.html>285457 is prime.</a>
<br>b^((n-1)/285457)-1 mod n = 4736697137797038905, which is a unit, inverse 64989482143271511135.
<p>(285457 * 294639853) divides n-1.
<p>(285457 * 294639853)^2 > n.
<p>n is prime by Pocklington's theorem.