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Re: the three limits of classical prime theory-> a contradiction

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  • Roger Bagula
    My mistake here was that: PrimePi[n]/CompositePi[n]=(1/Log[n])/(1-1/Log[n])=1/(Log[n]-1) That checks to give: PrimePi[n]=n/Log[n] I had the ratio not the
    Message 1 of 4 , Nov 4, 2003
      My mistake here was that:
      PrimePi[n]/CompositePi[n]=(1/Log[n])/(1-1/Log[n])=1/(Log[n]-1)
      That checks to
      give:
      PrimePi[n]=n/Log[n]
      I had the ratio not the density.
      I'm sorry.

      Roger Bagula wrote:

      > 1) Limit[Prime[n], n--> Infinity]=n*Log[n] ( Euler, I think)
      > 2) Limit[PrimePi[n],n->Infinity]=n/Log[n] (Hadamard)
      > 3) Limit[PrimePi[n]/CompositePi[n],n-> Infinity]=1/Log[n] ( from
      > Ulam, in both books I have by him)
      >
      > How 3) can be made to contradict 2):
      > PrimePi[n]+CompositePi[n]=n
      > PrimePi[n]/CompositePi[n]=PrimePi[n]/(n-PrimePi[n])=1/Log[n]
      > Solving for
      > PrimePi[n]=n/(1+Log[n])
      >
      > I'm puzzled by this which I found this morning.
      >

      --
      Respectfully, Roger L. Bagula
      tftn@..., 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
      URL : http://home.earthlink.net/~tftn
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