Primality proof for n = 27457:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=13.html>13 is prime.</a>
<br>b^((n-1)/13)-1 mod n = 22508, which is a unit, inverse 18902.
<p><a href=11.html>11 is prime.</a>
<br>b^((n-1)/11)-1 mod n = 102, which is a unit, inverse 15882.
<p><a href=3.html>3 is prime.</a>
<br>b^((n-1)/3)-1 mod n = 3587, which is a unit, inverse 17108.
<p>(3 * 11 * 13) divides n-1.
<p>(3 * 11 * 13)^2 > n.
<p>n is prime by Pocklington's theorem.