Primality proof for n = 275027:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=8089.html>8089 is prime.</a>
<br>b^((n-1)/8089)-1 mod n = 32601, which is a unit, inverse 230037.
<p>(8089) divides n-1.
<p>(8089)^2 > n.
<p>n is prime by Pocklington's theorem.