Primality proof for n = 27213313:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=2531.html>2531 is prime.</a>
<br>b^((n-1)/2531)-1 mod n = 4345717, which is a unit, inverse 26812476.
<p><a href=7.html>7 is prime.</a>
<br>b^((n-1)/7)-1 mod n = 24913557, which is a unit, inverse 13198165.
<p>(7 * 2531) divides n-1.
<p>(7 * 2531)^2 > n.
<p>n is prime by Pocklington's theorem.