Primality proof for n = 442454434174541737154207748628961512007:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=79879924901292653287162734017.html>79879924901292653287162734017 is prime.</a>
<br>b^((n-1)/79879924901292653287162734017)-1 mod n = 420732389808060423079108721936000878062, which is a unit, inverse 222735509909691272560813252787470476308.
<p>(79879924901292653287162734017) divides n-1.
<p>(79879924901292653287162734017)^2 > n.
<p>n is prime by Pocklington's theorem.