Primality proof for n = 727169:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=23.html>23 is prime.</a>
<br>b^((n-1)/23)-1 mod n = 363871, which is a unit, inverse 227161.
<p><a href=19.html>19 is prime.</a>
<br>b^((n-1)/19)-1 mod n = 126065, which is a unit, inverse 189376.
<p><a href=13.html>13 is prime.</a>
<br>b^((n-1)/13)-1 mod n = 460982, which is a unit, inverse 337377.
<p>(13 * 19 * 23) divides n-1.
<p>(13 * 19 * 23)^2 > n.
<p>n is prime by Pocklington's theorem.