Primality proof for n = 1919519569386763:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=8574133.html>8574133 is prime.</a>
<br>b^((n-1)/8574133)-1 mod n = 1059928654987440, which is a unit, inverse 1290547218147893.
<p><a href=127.html>127 is prime.</a>
<br>b^((n-1)/127)-1 mod n = 576774792492621, which is a unit, inverse 1870148777187772.
<p>(127 * 8574133) divides n-1.
<p>(127 * 8574133)^2 > n.
<p>n is prime by Pocklington's theorem.