137438953481

This number is a prime.

13 7438953481

Bertrand's postulate implies that there are infinitely many numbers a for which floor(2^a), floor(2^{2^a}), floor(2^{2^{2^a}}), ... are all prime. The smallest of these is a = 1.25164 75977 90463 01759 44320 53623... and generates the Bertrand primes: 2, 5, 37, 137438953481, .... The next Bertrand prime has 41,373,247,571 digits. [Caldwell]