Primality proof for n = 1740482054401:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=127139.html>127139 is prime.</a>
<br>b^((n-1)/127139)-1 mod n = 1394778125770, which is a unit, inverse 931889182908.
<p><a href=31.html>31 is prime.</a>
<br>b^((n-1)/31)-1 mod n = 728278689886, which is a unit, inverse 762457334809.
<p>(31 * 127139) divides n-1.
<p>(31 * 127139)^2 > n.
<p>n is prime by Pocklington's theorem.