Primality proof for n = 27093605140967:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=157427.html>157427 is prime.</a>
<br>b^((n-1)/157427)-1 mod n = 22383086807723, which is a unit, inverse 21416025351333.
<p><a href=11393.html>11393 is prime.</a>
<br>b^((n-1)/11393)-1 mod n = 19409880122647, which is a unit, inverse 11155190081724.
<p>(11393 * 157427) divides n-1.
<p>(11393 * 157427)^2 > n.
<p>n is prime by Pocklington's theorem.