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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 em
by ctdonath 13y ago
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)
- gizmo686 13y ago>2^(2^(2^...-1)-1)-1 seems prime for all nestings, but the numbers get enormous fast 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.
- crygin 13y agoThe issue is that we have no proof that they are primes in general, and they become large so quickly that verifying their primehood is (currently) impossible.
- gizmo686 13y agoFair enough, but the way I am reading your sequence still looks like it is all ones.
- anonymous 13y agoThe issue gizmo and I see with the sequence is that it is all ones if the first element is 2 - 1 = 1. 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.
- ErsatzVerkehr 13y agoMersenne primes whose exponents are themselves Mersenne primes.
- ctdonath 13y agoThink recursive Mersenne primes.