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25528Brun's constant in a different context

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  • anastasis_1999
    Apr 2 5:57 PM
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      hi
      so I've been trying for awhile to write an asymptotic formula for
      sum p_n<=x 1/(p_n - p(n-1))
      (the sum of reciprocals of prime gaps)
      where p_n means nth prime and n>1.

      my attempt is this
      x/ln(x)^2*(A*ln(ln(X))+(B*C_twin))+err.term, C_twin=0.66016...
      where A=approx 0.37787 and B is Brun's constant.
      The value of A is ln(2*C_twin)+1/10, and the error term is very small even for large x. Can someone verify this please? I can send you a spreadsheet if you like, I've tested this up to 500,000..
      thanks from Guy
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