Primality proof for n = 50380057830419:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=501783409.html>501783409 is prime.</a>
<br>b^((n-1)/501783409)-1 mod n = 36507808164655, which is a unit, inverse 3478089504644.
<p>(501783409) divides n-1.
<p>(501783409)^2 > n.
<p>n is prime by Pocklington's theorem.