Primality proof for n = 53308853141:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=2665442657.html>2665442657 is prime.</a>
<br>b^((n-1)/2665442657)-1 mod n = 1048575, which is a unit, inverse 10565125057.
<p>(2665442657) divides n-1.
<p>(2665442657)^2 > n.
<p>n is prime by Pocklington's theorem.