Primality proof for n = 27301809421:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=139537.html>139537 is prime.</a>
<br>b^((n-1)/139537)-1 mod n = 8454877314, which is a unit, inverse 19222083206.
<p><a href=1087.html>1087 is prime.</a>
<br>b^((n-1)/1087)-1 mod n = 20413604198, which is a unit, inverse 25471735842.
<p>(1087 * 139537) divides n-1.
<p>(1087 * 139537)^2 > n.
<p>n is prime by Pocklington's theorem.