Primality proof for n = 51854008820489653721386166877183100314125013148827513519511:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=2205934966343040556770938144460047174606142921998789.html>2205934966343040556770938144460047174606142921998789 is prime.</a>
<br>b^((n-1)/2205934966343040556770938144460047174606142921998789)-1 mod n = 1678854339195096945119834877480722652308433034646920790080, which is a unit, inverse 22569559802077454092244485144894145751950115599146260719372.
<p>(2205934966343040556770938144460047174606142921998789) divides n-1.
<p>(2205934966343040556770938144460047174606142921998789)^2 > n.
<p>n is prime by Pocklington's theorem.