Primality proof for n = 275168401:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=569.html>569 is prime.</a>
<br>b^((n-1)/569)-1 mod n = 130544397, which is a unit, inverse 115721881.
<p><a href=31.html>31 is prime.</a>
<br>b^((n-1)/31)-1 mod n = 265464192, which is a unit, inverse 122575355.
<p>(31 * 569) divides n-1.
<p>(31 * 569)^2 > n.
<p>n is prime by Pocklington's theorem.