Primality proof for n = 4221402400821188431:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=2468656374749233.html>2468656374749233 is prime.</a>
<br>b^((n-1)/2468656374749233)-1 mod n = 672456500494415253, which is a unit, inverse 2991756357733039994.
<p>(2468656374749233) divides n-1.
<p>(2468656374749233)^2 > n.
<p>n is prime by Pocklington's theorem.