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A goldbach conjecture for triplet primes

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  • d.broadhurst@open.ac.uk
    ... Sorry, Phil. I was rushing to get my check ... to reach msg #4208, and forgot that you had said the above in #4164. Conjecture: The largest even integer
    Message 1 of 6 , Nov 30, 2001
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      Phil reminded us of his question:

      > HAve you tried densities similar to those of twin primes,
      > (1/ln(n)^2), or higher power ln expressions (all denser
      > than the n^(1/a) spacings in the long run, but we don't
      > have the CPU power to exhaustively check anything but the
      > initial billion or so, which is a small number).

      Sorry, Phil. I was rushing to get my check
      > 4204,4206,4208]
      to reach msg #4208, and forgot that you had said the above in #4164.

      Conjecture: The largest even integer that is not
      the sum of two triplet primes is 7400384

      David
    • Phil Carmody
      ... Grin - pedant warning! Which triples? {0,2,6} or {0,4,6}, or either? ... It matters not - 7 million s far too low. I take your conjecture, and raise it
      Message 2 of 6 , Nov 30, 2001
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        On Fri, 30 November 2001, d.broadhurst@... wrote:
        > Conjecture: The largest even integer that is not
        > the sum of two triplet primes is 7400384

        Grin - pedant warning!
        Which triples? {0,2,6} or {0,4,6}, or either?
        :-)

        It matters not - 7 million's far too low. I take your conjecture, and raise it "only triplet primes not of the form 6n", i.e. the _middles_ alone. (+2+4, +4+4 and +2+2 do cover the three residues mod six, so we're alright.)

        No I haven't got a lower bound, but then again I'm sat in front of a pathetic machine which came shipped with _no_ compiler as standard, bizarre! If noone does the donkey-work for me, I am of course prepared to do it myself.

        Phil

        Don't be fooled, CRC Press are _not_ the good guys.
        They've taken Wolfram's money - _don't_ give them yours.
        http://mathworld.wolfram.com/erics_commentary.html


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      • d.broadhurst@open.ac.uk
        Phil Carmody ... I took my defn from Chris Caldwell, so the answer is: either. Defn: A prime triple is three consecutive primes, such that the first and the
        Message 3 of 6 , Nov 30, 2001
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          Phil Carmody

          > Which triples? {0,2,6} or {0,4,6}, or either?

          I took my defn from Chris Caldwell, so the answer is: either.

          Defn: A prime triple is three consecutive primes,
          such that the first and the last differ by six.

          Defn: A prime p is a triplet prime if and only if
          it belongs to a prime triple.

          Conjecture: The largest even integer that is not
          the sum of two triplet primes is 7400384

          I tried only up to sum=10^8
          with ZERO checking :-(

          David
        • d.broadhurst@open.ac.uk
          Phil Carmody ... I repeated the calculation leaving out all primes divisible by 6. It apears that the conclusion is unchanged. David:-)
          Message 4 of 6 , Dec 1, 2001
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            Phil Carmody
            > I take your conjecture, and raise it
            > "only triplet primes not of the form 6n",
            I repeated the calculation leaving out
            all primes divisible by 6.
            It apears that the conclusion is unchanged.
            David:-)
          • d.broadhurst@open.ac.uk
            Phil: As for triplet middles : try the analyis mod 30. David
            Message 5 of 6 , Dec 1, 2001
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              Phil: As for "triplet middles": try the analyis mod 30. David
            • Phil Carmody
              ... As you may have worked out - I did have my doubts, then I had my doubts about my doubts :-|. However, I m convinced that for at least 10 minutes last night
              Message 6 of 6 , Dec 1, 2001
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                On Sat, 01 December 2001, d.broadhurst@... wrote:

                >
                > Phil: As for "triplet middles": try the analyis mod 30. David

                As you may have worked out - I did have my doubts, then I had my doubts about my doubts :-|. However, I'm convinced that for at least 10 minutes last night I was actualy correct, evem if for the wrong reason.

                Explicitly:
                1 5 7 5 alone
                5 7 11 7 alone
                7 11 13 30n+11
                11 13 17 30n+13
                13 17 19 30n+17
                17 19 23 30n+19
                Therefore the gamut of sums is
                30n + { 0, 4, 6, 8, 22, 24, 26, 28 }
                and occasional 30n + { 16, 18, 20 }
                Which falls somewhat short of the mark.

                Oh well.

                Phil

                Don't be fooled, CRC Press are _not_ the good guys.
                They've taken Wolfram's money - _don't_ give them yours.
                http://mathworld.wolfram.com/erics_commentary.html


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