Primality proof for n = 274177:
<p>Take b = 5.
<p>b^(n-1) mod n = 1.
<p><a href=17.html>17 is prime.</a>
<br>b^((n-1)/17)-1 mod n = 216811, which is a unit, inverse 219983.
<p><a href=7.html>7 is prime.</a>
<br>b^((n-1)/7)-1 mod n = 2008, which is a unit, inverse 111282.
<p><a href=3.html>3 is prime.</a>
<br>b^((n-1)/3)-1 mod n = 135452, which is a unit, inverse 137633.
<p>(3^2 * 7 * 17) divides n-1.
<p>(3^2 * 7 * 17)^2 > n.
<p>n is prime by Pocklington's theorem.