24418Re: [PrimeNumbers] binary digit frequency in primes
- Aug 30, 2012--- On Thu, 8/30/12, James J Youlton Jr <youjaes@...> wrote:
> the primes, written in binary, all have the first bit set toDirichlet proved that all non-trivial residues are equally represented in the primes. So there are the same number of 4n+1 and 4n+3 primes.
> one and the last bit set to one except for the first prime
> “2”. what about the bits in the middle? is
> there a listing anywhere of the frequency of 1’s and
> 0’s of the inner bits? with analysis such even
> numbered bits vs. odd ones, and/or for just the prime
> numbered bits? I’m just curious...
Therefore the 2s bit is uniform.
Ditto 8n+1, 8n+3, 8n+5, and 8n+7, thus the 4s bit is uniform.
Ditto in aeternum ...
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