Let's say we are given the numbers 2, 2^2, 2^(2^2), 2^(2^(2^2)), and so on. Would all these numbers plus one be a prime number? (So far I see that 2^(2^(2*2)) or 2^16 works, but sadly 2^65536 is a little harder)

No, they are all not primes.

i.e 2^{256}-1 is not prime.

But, Mersenne primes have the form

2^{p}-1, where p is prime.

See here:

The UCLA Mersenne Prime (http://www.math.ucla.edu/~edson/prime/)

Um... it's 'plus' one and not minus one... but then, I don't know...

Wolfram alpha gave the digit as a 19729 digit number :eek: