Primality proof for n = 2053232229649:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=52357003.html>52357003 is prime.</a>
<br>b^((n-1)/52357003)-1 mod n = 1882278048204, which is a unit, inverse 498966283436.
<p>(52357003) divides n-1.
<p>(52357003)^2 > n.
<p>n is prime by Pocklington's theorem.