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New Math. Constant

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  • Sebastian Martin
    Hello: I found a new mathematical constant. Can someone find some algebraic relation with other constants? F[n_]:=
    Message 1 of 3 , Oct 27, 2008
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      Hello:

      I found a new mathematical constant.
      Can someone find some algebraic relation with other constants?


      F[n_]:=
      Product[(Prime[i]-1)/2,{i,3,n,2}]*Product[(Prime[i]+1)/2,{i,2,n,2}]/
      (Product[(Prime[i]+1)/2,{i,3,n,2}]*Product[(Prime[i]-1)/2,{i,2,n,2}])

      (The last one 2 means step 2)


      Do[Print[N[F[n],15]],{n,1000000,1004000,1000}]

      1.62172686861764
      1.62172686850817
      1.62172686840166
      1.62172686829112
      1.62172686818162




      [Non-text portions of this message have been removed]
    • Mark Underwood
      ... It looks like you started the primes at 3, rather than 2. (And, the dividing by two thing is unnecessary.) If you started at 2 or 5 or 7 ect, you would
      Message 2 of 3 , Nov 5, 2008
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        --- In primenumbers@yahoogroups.com, Sebastian Martin <sebi_sebi@...> wrote:
        >
        >
        >
        > Hello:
        >
        > I found a new mathematical constant.
        > Can someone find some algebraic relation with other constants?
        >
        >
        > F[n_]:=
        > Product[(Prime[i]-1)/2,{i,3,n,2}]*Product[(Prime[i]+1)/2,{i,2,n,2}]/
        > (Product[(Prime[i]+1)/2,{i,3,n,2}]*Product[(Prime[i]-1)/2,{i,2,n,2}])
        >
        > (The last one 2 means step 2)
        >
        >
        > Do[Print[N[F[n],15]],{n,1000000,1004000,1000}]
        >
        > 1.62172686861764
        > 1.62172686850817
        > 1.62172686840166
        > 1.62172686829112
        > 1.62172686818162
        >


        It looks like you started the primes at 3, rather than 2. (And, the dividing by two thing is
        unnecessary.) If you started at 2 or 5 or 7 ect, you would have obtained other constants.
        So, I don't think the constant you obtained is anything more special than the other ones
        that could be produced. So many constants, so little time. Speaking of constants, thank
        goodness for some willingness to *change* shown by our neighbours to the south last
        night.

        Mark
      • David Broadhurst
        ... Amen to that. I left this group in April 2003, shortly after posting http://tech.groups.yahoo.com/group/primenumbers/message/12037 I now feel able to
        Message 3 of 3 , Nov 9, 2008
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          --- In primenumbers@yahoogroups.com,
          "Mark Underwood" <mark.underwood@...> wrote:

          > Speaking of constants, thank goodness for some willingness
          > to *change* shown by our neighbours to the south last night.

          Amen to that.

          I left this group in April 2003, shortly after posting
          http://tech.groups.yahoo.com/group/primenumbers/message/12037

          I now feel able to return, for reasons unrelated to number theory,
          though I do not expect to contribute anything of mathematical
          substance before 20th January 2009.

          David Broadhurst
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