Primality proof for n = 4019927965686165521481374447:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=38818558648101949187.html>38818558648101949187 is prime.</a>
<br>b^((n-1)/38818558648101949187)-1 mod n = 2567203978082174180542092465, which is a unit, inverse 1985617555502541601781729247.
<p>(38818558648101949187) divides n-1.
<p>(38818558648101949187)^2 > n.
<p>n is prime by Pocklington's theorem.