Primality proof for n = 142215960774543971001476431146737:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=638388514873056719.html>638388514873056719 is prime.</a>
<br>b^((n-1)/638388514873056719)-1 mod n = 3288064302856747668832939769135, which is a unit, inverse 58663984612053960552168064006661.
<p>(638388514873056719) divides n-1.
<p>(638388514873056719)^2 > n.
<p>n is prime by Pocklington's theorem.