Primality proof for n = 6114313750387749125096789:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=139759026803824079.html>139759026803824079 is prime.</a>
<br>b^((n-1)/139759026803824079)-1 mod n = 3571720895531559946754220, which is a unit, inverse 4167520736099234533999317.
<p>(139759026803824079) divides n-1.
<p>(139759026803824079)^2 > n.
<p>n is prime by Pocklington's theorem.