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24022prime_n^(1/n) – prime_(n+1)^(1/(n+1))

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  • John W. Nicholson
    Feb 2, 2012
      a := sum ({n,1,k}, prime_n^(1/n) – prime_(n+1)^(1/(n+1))) ,  {n,1,k} means n=1 to k.
      For k <= 1,000,000, observe a < 1, and a-->1.

      What is the largest k tested? Does a >1 ever happen? What does this imply if it does or does not happen? Can this be proved?
      John W. Nicholson

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