Primality proof for n = 1997278224258685136359:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=7287687546097909.html>7287687546097909 is prime.</a>
<br>b^((n-1)/7287687546097909)-1 mod n = 1961774936192948263648, which is a unit, inverse 1063789206124488227763.
<p>(7287687546097909) divides n-1.
<p>(7287687546097909)^2 > n.
<p>n is prime by Pocklington's theorem.