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The Prime of Primes

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  • miltbrown@earthlink.net
    Prime of Primes p(1)=2=x1 p(2)=3=x2 p(3)=5=x3 p(5)=11=x4 p(11)=31=x5 p(31)=127=x6 p(127)=709=x7 p(709)=5381=x8 p(5381)=??=x9 ... p(n)~n*ln(n) General Formula
    Message 1 of 2 , Jun 30, 2006
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      Prime of Primes

      p(1)=2=x1
      p(2)=3=x2
      p(3)=5=x3
      p(5)=11=x4
      p(11)=31=x5
      p(31)=127=x6
      p(127)=709=x7
      p(709)=5381=x8
      p(5381)=??=x9
      ...
      p(n)~n*ln(n)

      General Formula Derivation

      p(xn)~xn*ln(xn)
      P(xn)~p(x(n-1))*ln(p(x(n-1)))
      p(xn)/p(x(n-1))~ln(p(x(n-1)))
      p(xn)/p(x(n-1))~ln(x(n-1))+ln(ln(x(n-1))))

      p(x(n-1))/p(x(n-2))~ln(p(x(n-2)))

      p(xn)/1~ln(p(x(n-1)))*ln(p(x(n-2)))...ln(2)

      p^n(1)~ln(p(x(n-1)))*ln(p(x(n-2)))...ln(2)

      p^n(y)~ln(p(x(n-1)))*ln(p(x(n-2)))...ln(p(y))


      p^n(1)~[ln(p(x(n-2)))+ln(ln(p(x(n-2))))]*ln(p(x(n-2)))...ln(2)
      p^n(1)~[ln^2(p(x(n-2)))+ln(ln(p(x(n-2))))*ln(p(x(n-2)))]...ln(2)
      ...

      Milton L. Brown
      miltbrown at earthlink.net
    • Dick
      ... I liked primeth primes better, a thread started by Werner D. Sand last November, starting with message 17225
      Message 2 of 2 , Jul 2, 2006
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        --- In primenumbers@yahoogroups.com, miltbrown@... wrote:
        >
        > Prime of Primes
        >
        > p(1)=2=x1
        > p(2)=3=x2
        > p(3)=5=x3
        > p(5)=11=x4
        > p(11)=31=x5
        > p(31)=127=x6
        > p(127)=709=x7
        > p(709)=5381=x8
        > p(5381)=??=x9

        I liked 'primeth primes' better, a thread started by Werner D. Sand
        last November, starting with message 17225

        http://groups.yahoo.com/group/primenumbers/message/17225

        A thread which you participated in Milton, do you remember?
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