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Re: [PrimeNumbers] Appropriate use of PNT?

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  • Andy Swallow
    ... Careful with this, you ve quoted the error term wrong. The PNT statement should be, #{x
    Message 1 of 2 , Oct 1, 2003
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      On Wed, Oct 01, 2003 at 09:27:31PM -0000, Adam wrote:
      > #{x<=N:x is prime}=N/log(N)+o(1).

      Careful with this, you've quoted the error term wrong. The PNT statement
      should be,

      #{x<=N:x is prime}=(N/log N)*(1+o(1))

      i.e. the o(1) is relative error, not absolute. Even on the Riemann
      hypothesis, the best error term that we could hope for is O(N^1/2). If
      the PNT was as you stated it, then there'd be a lot less 'roughness' to
      your calculations...

      Andy
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