Primality proof for n = 213441916511:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=292386187.html>292386187 is prime.</a>
<br>b^((n-1)/292386187)-1 mod n = 47282696164, which is a unit, inverse 209712463866.
<p>(292386187) divides n-1.
<p>(292386187)^2 > n.
<p>n is prime by Pocklington's theorem.