Primality proof for n = 426632512014427833817:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=23314383343543.html>23314383343543 is prime.</a>
<br>b^((n-1)/23314383343543)-1 mod n = 53960818949260564655, which is a unit, inverse 62814440624553491211.
<p>(23314383343543) divides n-1.
<p>(23314383343543)^2 > n.
<p>n is prime by Pocklington's theorem.