Primality proof for n = 243585722668023007729:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=6514380687527359.html>6514380687527359 is prime.</a>
<br>b^((n-1)/6514380687527359)-1 mod n = 58062397257690082651, which is a unit, inverse 51166098697536523084.
<p>(6514380687527359) divides n-1.
<p>(6514380687527359)^2 > n.
<p>n is prime by Pocklington's theorem.