Primality proof for n = 18911:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=61.html>61 is prime.</a>
<br>b^((n-1)/61)-1 mod n = 5233, which is a unit, inverse 6129.
<p><a href=31.html>31 is prime.</a>
<br>b^((n-1)/31)-1 mod n = 18552, which is a unit, inverse 15487.
<p>(31 * 61) divides n-1.
<p>(31 * 61)^2 > n.
<p>n is prime by Pocklington's theorem.