Primality proof for n = 8312956054562778877481:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=1019532643.html>1019532643 is prime.</a>
<br>b^((n-1)/1019532643)-1 mod n = 1622789414516127142474, which is a unit, inverse 7349153878600622169760.
<p><a href=208393.html>208393 is prime.</a>
<br>b^((n-1)/208393)-1 mod n = 2460496464207392644677, which is a unit, inverse 495907208976900334963.
<p>(208393 * 1019532643) divides n-1.
<p>(208393 * 1019532643)^2 > n.
<p>n is prime by Pocklington's theorem.