Primality proof for n = 12779357438669681:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=324689.html>324689 is prime.</a>
<br>b^((n-1)/324689)-1 mod n = 4006238619156740, which is a unit, inverse 1987457366776900.
<p><a href=15823.html>15823 is prime.</a>
<br>b^((n-1)/15823)-1 mod n = 7013642631440734, which is a unit, inverse 1534361525383712.
<p>(15823 * 324689) divides n-1.
<p>(15823 * 324689)^2 > n.
<p>n is prime by Pocklington's theorem.