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A semi-empirical prime like function with primes isolated [Fwd: SEQ FROM Roger L. Bagula]

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  • Roger Bagula
    I developed three new entropy like prime functions ( two constants) to get a very good linear agreement with the primes up to 1000, based on the entropy
    Message 1 of 1 , Dec 3, 2003
      I developed three new entropy like prime functions ( two constants) to
      get a very good linear agreement with the primes
      up to 1000, based on the entropy content of the primes.
      I get an entropy constant very near:
      3-E
      The Prime based constant:
      z0=Sum[PrimePi[n]/(n*Prime[n]),{n,1,Infinity}]
      is very interesting as it increases the entropy as 1/n!
      Since it is based on entropy development
      this function should work even at very large
      primes.

      -------- Original Message --------
      Subject: SEQ FROM Roger L. Bagula
      Date: Wed, 3 Dec 2003 10:51:43 -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 3,5,11,79,109,131,211,223,229,241,271,277,347,353,379,443,463,509,523,557,571,
      577,631,727,827,877,971,1051,1103,1229,1237,1259,1303,1409,1439,1447,1493,
      1531,1669,1723,1747,1801,1847,1871,1979,1987,2081,2089,2113,2129,2137,2207,
      2239,2287,2311,2351,2383,2593,2609,2617,2699,2707,2731,2837,2861,3041,3049,
      3181,3271,3313,3329,3469,3527,3593,3643,3659,3701,3709,3767,3851,3917,4001,
      4027,4111,4273,4349,4409,4451,4639,4673,4723,4783,4817,4877,4903,4937,5039,
      5081,5107,5167,5209,5261,5303,5381,5441,5449,5501,5527,5639,5657,5683,5717,
      5743,5821,6029,6037,6133,6151,6203,6229,6247,6299,6317,6343,6361,6553,6571,
      6737,6781,6869,6983,7027,7079,7159,7229,7247,7309,7433,7451,7477,7681,7699,
      7717,7753,7841,7877,7993
      %N A000001 A semi-empirical prime like function with primes isolated
      %C A000001 The Wanged it function:
      p[n_]=Sum[-Log[PrimePi[i]/i],{i,2,n}]
      Is a new type of Prime function that represents the build up of entropy in the
      Primes.
      Also the constant is approximately five( or w0~3-E):
      2+E+w0~5
      %F A000001 p[n_]=Sum[-Log[PrimePi[i]/i],{i,2,n}]
      a=Table[If[PrimeQ[Floor[p[n]*(2+E+z0/n+w0)]]==True,Floor[p[n]*(2+E+z0/n+w0)],
      0],{n,2,1000}]
      %t A000001 (*first entropy constant to n=10000*)
      p0[n_]=PrimePi[n]/n
      a=Table[-p0[n]*Log[p0[n]],{n,2,10000}];
      w0=N[Apply[Plus,a],200]/10000
      (*Second entropy constant to n=10000*)
      z0=Sum[PrimePi[n]/(n*Prime[n]),{n,1,10000}];
      (* semi-empirical prime-like function based on prime entropy sums*)
      p[n_]=Sum[-Log[PrimePi[i]/i],{i,2,n}]
      a0=Table[If[PrimeQ[Floor[p[n]*(2+E+z0/n+w0)]]==True,Floor[p[n]*(2+E+z0/n+w0)],
      0],{n,2,1000}];
      c0=Delete[Union[a0],1]
      %O A000001 2
      %K A000001 ,nonn,
      %A A000001 Roger L. Bagula (tftn@...), Dec 03 2003
      RH
      RA 209.179.57.236
      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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