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Building Twin Primes II

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  • Milton Brown
    All twin primes after (29,31) are built as 30*k + (11,13) or +(17,19) or +(29,31) Attached is a table for k from 1 to 20 showing their construction. The
    Message 1 of 6 , Jun 8, 2005
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      All twin primes after (29,31) are built as 30*k + (11,13) or +(17,19) or +(29,31)

      Attached is a table for k from 1 to 20 showing their construction.

      The assertion is that for every k which is prime, there is at least one
      of the 3 additions which produces a twin prime.

      (30)k +(11,13) -------+(17,19) ------+(29,31)
      =================================
      1 -------(41,31) --------(47,49x)------- (59,61)
      2p -----(71,73) --------(77x,79) -------(89,91x)
      3p ----(101,103) -----(107,109) -----(119x,121x)
      4 ------(131,133x) ----(137,139) -----(149,151)
      5p ----(161x,163) ----(167,169x) ----(179,181)

      6 ------(191,193) ------(197,199) -----(209x,211)
      7p ----(221x,223) -----(227,229) ----(239,241)
      8 ------(251,253x) -----(257,259x) ---(269,271)
      9 ------(281,283) ------(287x,289x) --(299x,301x)
      10 ----(311,313) ------(317,319x) ----(329x,331)

      11p --(341x,343x) ---(347,349) -----(359,361x)
      12 ----(371x,373) -----(377x,379) ---(389,391x)
      13p --(401,403x) -----(407x,409) ---(419,421)
      14 ----(431,433) -------(437x,439) ---(449,451x)
      15 ----(461,463) -------(467,469x) ---(479,481x)

      16 ----(491,493x) ------(497x,499) --(509,511x)
      17p --(521,523) -------(527x,529x) -(539x,541)
      18 ----(551x,553x) ----(557,559x) ---(569,571)
      19 p -(581x,583x) -----(587,589x) --(599,601)
      20 ----(611x,613) ------(617,619) ----(627x,631)


      Milton L. Brown

      [Non-text portions of this message have been removed]
    • Jud McCranie
      ... Isn t that the same thing as saying that they are either 11 & 13, or 17 & 19, or 29 & 31 mod 30?
      Message 2 of 6 , Jun 8, 2005
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        At 06:04 PM 6/8/2005, Milton Brown wrote:
        >All twin primes after (29,31) are built as 30*k + (11,13) or +(17,19) or
        >+(29,31)

        Isn't that the same thing as saying that they are either 11 & 13, or 17 &
        19, or 29 & 31 mod 30?
      • Milton Brown
        Yes, obviously. And, you point is?
        Message 3 of 6 , Jun 8, 2005
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          Yes, obviously.

          And, you point is?


          > [Original Message]
          > From: Jud McCranie <j.mccranie@...>
          > To: <miltbrown@...>
          > Cc: primenumbers <primenumbers@yahoogroups.com>
          > Date: 6/8/2005 7:29:38 PM
          > Subject: Re: [PrimeNumbers] Building Twin Primes II
          >
          > At 06:04 PM 6/8/2005, Milton Brown wrote:
          > >All twin primes after (29,31) are built as 30*k + (11,13) or +(17,19) or
          > >+(29,31)
          >
          > Isn't that the same thing as saying that they are either 11 & 13, or 17 &
          > 19, or 29 & 31 mod 30?
          >
          >
          >
          >
          >
          >
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          > The Prime Pages : http://www.primepages.org/
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        • andrew_j_walker
          You ve only tested for 8 prime values below, a lot more are needed before we can make assertions. Andrew ... +(17,19) or +(29,31)
          Message 4 of 6 , Jun 8, 2005
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            You've only tested for 8 prime values below, a lot more are needed before
            we can make assertions.

            Andrew
            --- In primenumbers@yahoogroups.com, "Milton Brown" <miltbrown@e...>
            wrote:
            > All twin primes after (29,31) are built as 30*k + (11,13) or
            +(17,19) or +(29,31)
            >
            > Attached is a table for k from 1 to 20 showing their construction.
            >
            > The assertion is that for every k which is prime, there is at least one
            > of the 3 additions which produces a twin prime.
            >
            > (30)k +(11,13) -------+(17,19) ------+(29,31)
            > =================================
            > 1 -------(41,31) --------(47,49x)------- (59,61)
            > 2p -----(71,73) --------(77x,79) -------(89,91x)
            > 3p ----(101,103) -----(107,109) -----(119x,121x)
            > 4 ------(131,133x) ----(137,139) -----(149,151)
            > 5p ----(161x,163) ----(167,169x) ----(179,181)
            >
            > 6 ------(191,193) ------(197,199) -----(209x,211)
            > 7p ----(221x,223) -----(227,229) ----(239,241)
            > 8 ------(251,253x) -----(257,259x) ---(269,271)
            > 9 ------(281,283) ------(287x,289x) --(299x,301x)
            > 10 ----(311,313) ------(317,319x) ----(329x,331)
            >
            > 11p --(341x,343x) ---(347,349) -----(359,361x)
            > 12 ----(371x,373) -----(377x,379) ---(389,391x)
            > 13p --(401,403x) -----(407x,409) ---(419,421)
            > 14 ----(431,433) -------(437x,439) ---(449,451x)
            > 15 ----(461,463) -------(467,469x) ---(479,481x)
            >
            > 16 ----(491,493x) ------(497x,499) --(509,511x)
            > 17p --(521,523) -------(527x,529x) -(539x,541)
            > 18 ----(551x,553x) ----(557,559x) ---(569,571)
            > 19 p -(581x,583x) -----(587,589x) --(599,601)
            > 20 ----(611x,613) ------(617,619) ----(627x,631)
            >
            >
            > Milton L. Brown
            >
            > [Non-text portions of this message have been removed]
          • Jud McCranie
            ... My point is - what is your point? Your observation says nothing new.
            Message 5 of 6 , Jun 8, 2005
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              At 01:07 AM 6/9/2005, Milton Brown wrote:
              >Yes, obviously.
              >
              >And, you point is?

              My point is - what is your point? Your observation says nothing new.
            • Jud McCranie
              ... Well, the first counterexample is k=23, (701,703) (707,709) (719,721) The next few counterexamples are 31, 37, 41, 61, 73, 83, 97.
              Message 6 of 6 , Jun 8, 2005
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                At 06:04 PM 6/8/2005, Milton Brown wrote:
                >All twin primes after (29,31) are built as 30*k + (11,13) or +(17,19) or
                >+(29,31)
                >
                >Attached is a table for k from 1 to 20 showing their construction.
                >
                >The assertion is that for every k which is prime, there is at least one
                >of the 3 additions which produces a twin prime.

                Well, the first counterexample is k=23,
                (701,703)
                (707,709)
                (719,721)

                The next few counterexamples are 31, 37, 41, 61, 73, 83, 97.
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