Primality proof for n = 27582403:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=23819.html>23819 is prime.</a>
<br>b^((n-1)/23819)-1 mod n = 22446835, which is a unit, inverse 18325768.
<p>(23819) divides n-1.
<p>(23819)^2 > n.
<p>n is prime by Pocklington's theorem.