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Re: on the number of primes in the interval of a given length

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  • andrey_601
    ... However, if the k-tuple conjecture holds, the lim sup will be O[d/log(d)]: http://mathworld.wolfram.com/k-TupleConjecture.html
    Message 1 of 2 , Aug 26, 2010
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      > and came to a conjecture:
      >
      > lim sup | pi(n+d) - pi(n) - integral(1/log(t), t from n to n+d) | = O[sqrt(d)]
      > where d and n are positive integers and lim sup is taken for n-->inf.

      However, if the k-tuple conjecture holds, the lim sup will be O[d/log(d)]:

      http://mathworld.wolfram.com/k-TupleConjecture.html
      http://www.opertech.com/primes/k-tuples.html
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