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my best prime generation function yet! [Fwd: SEQ FROM Roger L. Bagula]

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  • Roger Bagula
    With a functional Shannon entropy power of N=1/log(n) this function misses the first three primes , but does very well in the lower primes after that.
    Message 1 of 1 , Jan 31, 2004
      With a functional Shannon entropy power of N=1/log(n)
      this function misses the first three primes ,
      but does very well in the lower primes after that.
      Derivation goes like this from Shannon's formula
      for the entropy power of white noise:
      N1=(1/2*Pi*E)*Exp(2*H)
      when ( linear transform of n to Prime[n] )
      H=Log(Prime[n]/n)
      then
      N1=(E/(2*Pi))*Prime[n]/n
      or
      Prime[n]=2*Pi*n*N/E
      and the asymptotic prime distribution function is:
      PrimePi[n]--> n/Log(n)
      which gives
      N=1/Log(n)
      as used here.

      -------- Original Message --------
      Subject: SEQ FROM Roger L. Bagula
      Date: Sat, 31 Jan 2004 16:23:44 -0500 (EST)
      From: <njas@...>
      Reply-To: tftn@...
      To: njas@...
      CC: tftn@...



      The following is a copy of the email message that was sent to njas
      containing the sequence you submitted.

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      This copy is just for your records. No reply is expected.
      Subject: NEW SEQUENCE FROM Roger L. Bagula


      %I A000001
      %S A000001 7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,
      109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,
      223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,
      331
      %N A000001 An entropy power of white noise function with N=1/log(n)
      %C A000001 Function is based on asymptotic form of distribution:
      PrimePi[n]--> n/log(n)
      Function misses the first three primes {2,3,5} , but is pretty good after that.
      %D A000001 Claude E. Shannon, The Mathematical Theory of Communications, page 63
      %F A000001 a(n) = if Floor[2*Pi*n/(E*Log[n])] is prime then Floor[2*Pi*n/(E*Log[m])]
      %t A000001 digits=5*200
      f[n_]=Floor[2*Pi*n/(E*Log[n])]
      a=Delete[Union[Table[If [PrimeQ[f[n]]==True,f[n],0],{n,2,digits}]],1]
      %O A000001 2
      %K A000001 ,nonn,
      %A A000001 Roger L. Bagula (tftn@...), Jan 31 2004
      RH
      RA 209.179.51.13
      RU
      RI



      --
      Respectfully, Roger L. Bagula
      tftn@..., 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
      URL : http://home.earthlink.net/~tftn
      URL : http://victorian.fortunecity.com/carmelita/435/




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