Primality proof for n = 41347742847751193213:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=1003679.html>1003679 is prime.</a>
<br>b^((n-1)/1003679)-1 mod n = 26706332448537466961, which is a unit, inverse 75295766380036379.
<p><a href=2837.html>2837 is prime.</a>
<br>b^((n-1)/2837)-1 mod n = 15393029802464470236, which is a unit, inverse 38003118359527610930.
<p><a href=569.html>569 is prime.</a>
<br>b^((n-1)/569)-1 mod n = 24449040016492572914, which is a unit, inverse 30813572042053864746.
<p>(569 * 2837 * 1003679) divides n-1.
<p>(569 * 2837 * 1003679)^2 > n.
<p>n is prime by Pocklington's theorem.