Primality proof for n = 163810856527:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=27301809421.html>27301809421 is prime.</a>
<br>b^((n-1)/27301809421)-1 mod n = 63, which is a unit, inverse 59803963494.
<p>(27301809421) divides n-1.
<p>(27301809421)^2 > n.
<p>n is prime by Pocklington's theorem.