Primality proof for n = 413244619895455989650825325680172591660047:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=20705423504133292078628634597817.html>20705423504133292078628634597817 is prime.</a>
<br>b^((n-1)/20705423504133292078628634597817)-1 mod n = 170427992298651566799657712128701333657406, which is a unit, inverse 171692952802543298859116009854306306676002.
<p>(20705423504133292078628634597817) divides n-1.
<p>(20705423504133292078628634597817)^2 > n.
<p>n is prime by Pocklington's theorem.