Primality proof for n = 19197701325821:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=41734133317.html>41734133317 is prime.</a>
<br>b^((n-1)/41734133317)-1 mod n = 17447704774951, which is a unit, inverse 17507678135042.
<p>(41734133317) divides n-1.
<p>(41734133317)^2 > n.
<p>n is prime by Pocklington's theorem.