Primality proof for n = 12397338596863679689524759770405177749801411:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=413244619895455989650825325680172591660047.html>413244619895455989650825325680172591660047 is prime.</a>
<br>b^((n-1)/413244619895455989650825325680172591660047)-1 mod n = 1073741823, which is a unit, inverse 302965702597983423679073862837973295262978.
<p>(413244619895455989650825325680172591660047) divides n-1.
<p>(413244619895455989650825325680172591660047)^2 > n.
<p>n is prime by Pocklington's theorem.