--- On Thu, 8/30/12, James J Youlton Jr <

youjaes@...> wrote:

> the primes, written in binary, all have the first bit set to

> 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...

Dirichlet 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.

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 ...

Phil

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