Primality proof for n = 2746144996771313789:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=15643211.html>15643211 is prime.</a>
<br>b^((n-1)/15643211)-1 mod n = 1155916230020495012, which is a unit, inverse 555212053675919679.
<p><a href=34483.html>34483 is prime.</a>
<br>b^((n-1)/34483)-1 mod n = 1595067458926635507, which is a unit, inverse 460538071750631915.
<p>(34483 * 15643211) divides n-1.
<p>(34483 * 15643211)^2 > n.
<p>n is prime by Pocklington's theorem.