Primality proof for n = 10019573:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=80803.html>80803 is prime.</a>
<br>b^((n-1)/80803)-1 mod n = 2007763, which is a unit, inverse 1014871.
<p>(80803) divides n-1.
<p>(80803)^2 > n.
<p>n is prime by Pocklington's theorem.