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A goldbach conjecture for triplet-middle primes

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  • d.broadhurst@open.ac.uk
    ... Phil used his fingers and toes ... Err, what have you got against 2 mod 30, Phil? Example: take 13 from {11, 13, 17} and 19 from (17, 19, 23) to make 13 +
    Message 1 of 3 , Dec 1, 2001
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      I wrote:

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

      Phil used his fingers and toes
      (and perhaps some, but not enough, of Anna's):

      > Therefore the gamut of sums is
      > 30n + { 0, 4, 6, 8, 22, 24, 26, 28 }

      Err, what have you got against 2 mod 30, Phil?

      Example: take 13 from {11, 13, 17}
      and 19 from (17, 19, 23)
      to make 13 + 19 = 32 = 2 mod 30

      Also sprach Rosinante:

      failed mod 30

      5700010 10
      5700012 12
      5700014 14
      5700016 16
      5700018 18
      5700020 20
      5700040 10
      5700042 12
      5700044 14
      5700046 16
      5700048 18
      5700050 20
      5700070 10
      5700072 12
      5700074 14
      5700076 16
      5700078 18
      5700080 20
      ....... ..

      Conjecture: The largest even number n whose residue mod 30
      is not in [10,20], with n not expressible as the sum of 2
      triplet-middles, is 12010144.

      David (stopped at 10^8)
    • d.broadhurst@open.ac.uk
      ... Exponentials are wonderful; they cut off real fast. Also sprach Rosinante failed 5751472 5823812 5950106 5972786 6025984 6112688 6168926 6246668 7226486
      Message 2 of 3 , Dec 1, 2001
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        > Conjecture: The largest even number n whose residue mod 30
        > is not in [10,20], with n not expressible as the sum of 2
        > triplet-middles, is 12010144.

        Exponentials are wonderful; they cut off real fast.
        Also sprach Rosinante

        failed

        5751472
        5823812
        5950106
        5972786
        6025984
        6112688
        6168926
        6246668
        7226486
        7310302
        7400392
        8267876
        8521976
        11078306
        11814566
        12010144

        [the rest is silence]
      • Phil Carmody
        ... I do, don t I :-) ... I find fingers and toes far superior to programs like Mathematica, but just this once Mathematica is capable of doing this vast
        Message 3 of 3 , Dec 2, 2001
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          On Sat, 01 December 2001, d.broadhurst@... wrote:
          > I wrote:
          >
          > > Phil: As for "triplet middles": try the analyis mod 30.
          >
          > Phil used his fingers and toes
          > (and perhaps some, but not enough, of Anna's):
          >
          > > Therefore the gamut of sums is
          > > 30n + { 0, 4, 6, 8, 22, 24, 26, 28 }
          >
          > Err,

          I do, don't I :-)

          > what have you got against 2 mod 30, Phil?
          > Example: take 13 from {11, 13, 17}
          > and 19 from (17, 19, 23)
          > to make 13 + 19 = 32 = 2 mod 30

          I find fingers and toes far superior to programs like Mathematica, but just this once Mathematica is capable of doing this vast computational feet better than my own digits. How bizarre.

          (sic, above, for reference)

          In[24]:=
          r30 = {11, 13, 17, 19}

          Out[24]=
          {11, 13, 17, 19}

          In[25]:=
          Union[Flatten[Outer[Mod[#1 + #2 , 30] &, r30, r30]]]

          Out[25]=
          {0, 2, 4, 6, 8, 22, 24, 26, 28}



          Shall we just say it was an off day...

          I'm glad that there's a post-processing filter which is able to extract some sense out of my gibberings. Ta muchly.


          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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