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Re: [PrimeNumbers] Prime distribution?

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  • Andy Swallow
    ... Number of primes between p and p^2 is asymptotically N=2*p^2*log p, so log N=2log p+log 2+loglog p. So obviously you re going to get a linear fit, for such
    Message 1 of 2 , Sep 29, 2014
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      > Consider a continuous list of primes starting 2 ie 2,3,5,7........p
      >
      > and N is the number of primes in the interval >p <p^2
      >
      > I've been plotting logN versus logp
      >
      > Thus far, I've used data up to p=317.
      >
      > This seems to be giving a very good linear fit
      >
      > I was wondering whether someone could help to see whether this still holds
      > for p>>317.

      Number of primes between p and p^2 is asymptotically N=2*p^2*log p, so
      log N=2log p+log 2+loglog p. So obviously you're going to get a linear
      fit, for such a small range. log N increases slightly faster than log p,
      but you'd have to plot a much larger range to appreciate the difference.

      Andy
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