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twinprime conjecture

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  • anastasis_1999
    hello, I ve been considering a twinprime analogy to the sum sum (n
    Message 1 of 1 , Jul 15, 2005
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      hello,

      I've been considering a twinprime analogy to the sum

      sum (n<=x) M(n)/n = log x+O(1)

      where M(n) is the Mangoldt function. My formula is this:

      f(x)=sum (2<n<=x, condition M(n)*M(n+2)<>0) M(n)/n = 2*H*loglog x
      +O(1)

      where H is the twinprime constant=0.66016...

      so that f(20)=log (3)/3+log(5)/5+log(7)/7+log(3)/9+log(11)/11+log
      (17)/17=1.472797 and for each added term in the sum it adds
      according to where the powers of prime pairs exist.

      I've tested this function for all x less than half a million, and it
      works fine.

      Comments, please.
      from Guy
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