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Re: Brun +

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  • Andrew Swallow
    ... is ... If the three separate sums converge, then the sum of all three will also converge... ... Difficult to tell. Removing every n th prime would still
    Message 1 of 2 , Jan 19, 2004
      --- In primenumbers@yahoogroups.com, "John W. Nicholson" <johnw.
      nicholson@s...> wrote:
      > Brun found that the sum of 1/twins is a constant. I am guessing that
      > cousins and sexies sums are simular in that they have constants too.
      > What I am wondering is if the 1/(sum of twins, cousins, and sexies)
      is
      > a constant?

      If the three separate sums converge, then the sum of all three will
      also converge...

      > If it is a constant, at what time does the of addition of
      > more terms, as to approach of the sum 1/(all primes), does the sum
      > become divergent? Maybe if a constant number of primes are removed
      > from the sum of pries, say every fifth prime or primeth prime?

      Difficult to tell. Removing every n'th prime would still leave a
      divergent sequence. Removing every prime'th prime? Would still
      diverge, since it's a more dense sequence than removing every n'th
      prime.

      > How about instead of the twins themselves the sums of the first
      primes
      > prior and after the twin? Like (1/2+1/7) + (1/3+1/11) + (1/7+1/17) +
      > (1/13+1/23)....

      Would still converge, since pretty much identical to the prime twin
      sum.

      Andy
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