My 3 favorites:
2^(2^(2^...-1)-1)-1 seems prime for all nestings, but the numbers get enormous fast
John Conway's "surreal numbers" create all math from an empty set
Fractals ('nuf said)
2^(2^(2^...-1)-1)-1 seems prime for all nestings, but the numbers get enormous fast
John Conway's "surreal numbers" create all math from an empty set
Fractals ('nuf said)
Can you explain this. I read your expression (with infinite nesting) as x=2^(x-1), whose solutions are 1 and 2.
Looking at it as a series, I see: 2-1=1 2^(2-1)-1=1 2^(2^(2-1)-1)-1=1 2^(2^(2^...-1)-1)-1=1
Also, assuming that a sequence does have the properties you describe (always prime, and gets large very fast), it seems like that sequence would either have to be hard to compute, or unknown to all of the mathematicians working on finding large primes.
Are you supposed to start with 2^2 - 1 = 3; then 2^3 - 1 = 7; 2^7 - 1 = 127; etc? Those do seem to be all prime.