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Every Prime Number > 5 can be expressed as the sum of . . .

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  • Bob Gilson
    I think it was Hardy or Littlewood who stated that any fool can come up with an unprovable Conjecture. So here s mine Every prime number 5 can be expressed
    Message 1 of 3 , Aug 24, 2014
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      I think it was Hardy or Littlewood who stated that any fool can come up with an unprovable Conjecture.

      So here's mine

      Every prime number > 5 can be expressed as the sum of ( ( a pair of twin primes ) / 2 ) + a prime number.

      Examples:

      7 = 4 + 3
      11= 6 + 5
      13 = 6 + 7
      17 = 12 + 5
      19 = 12 + 7
      23 = 12 + 11
      29 = 18 + 11
      31 = 18 + 13
      37 = 30 + 7
      41 = 30 + 11
      43 = 30 + 13
      47 = 42 + 5
      53 = 42 + 11
      59 = 42 + 17
      61 = 42 + 19
      67 = 60 + 7
      71 = 60 + 11
      73 = 60 + 13
      79 = 60 + 19
      83 = 60 + 23
      89 = 60 + 29
      97 = 60 + 37
      101 = 72 + 29

      etc . . .

      I am sure my Conjecture cannot be original ( but I wish! ), and perhaps someone knows of counter examples and previous investigations into the subject.

      Thanks as always

      Bob
    • Luis Rodriguez
      Sure. There are sufficient differences between primes to be pairing with the  even numbers resulting from the mean of two twin primes. The list of means of
      Message 2 of 3 , Aug 25, 2014
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        Sure. There are sufficient differences between primes to be pairing with the  even numbers resulting from the mean of two twin primes.
        The list of means of two twin primes are:
        4,6,12,18,30,42,50,72,102,....
        Its impossible that never we will find a difference between two primes that cannot be one of that list.
        Ludovicus

      • Luis Rodriguez
        Here is an heuristic argument in behalf of the conjecture: The twin primes results from the pairing of the following A.P. 6n  - 1 = 5   11  17  23  29 
        Message 3 of 3 , Aug 25, 2014
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          Here is an heuristic argument in behalf of the conjecture:

          The twin primes results from the pairing of the following A.P.
          6n  - 1 = 5   11  17  23  29  35  41  47  53  59  65 .....
          6n + 1 = 7   13  19  25  31  37  43  49  55  61  67 .....

          Mean  = 6   12  18        30        42              60  ...

          Also with the mean (3 + 5) / 2 = 4 , I have the available differences:
          4 , 6 , 12 , 18 ,  30 , 42 , 60 ,  72 ... (4 & Multiples of 6)

          The prime numbers >= 5  are contained in the sequence:
          5  7  11  13  17  19   23   25  29  31  35  37  41  43  47  49  ...
          (With differences: 2 , 4 , 2 , 4 , 2 , 4 ....)

          That is: With this differences I can compose the available differences  and summing it, from each prime , I can reach another prime. So:
           5  + 6  = 11
           7  + 4  = 11
          11 + 6  = 17
          13 + 4  = 17
          17 + 6  = 23
          19 + 4  = 23
          23 + 6  = 29
          29 +12 = 41
          31 + 6  = 37
          . . . . . . . . .
          113 + 18  = 131
          . . . . . . . . .




          El Lunes 25 de agosto de 2014 8:36, Luis Rodriguez <luiroto@...> escribió:


          Sure. There are sufficient differences between primes to be pairing with the  even numbers resulting from the mean of two twin primes.
          The list of means of two twin primes are:
          4,6,12,18,30,42,50,72,102,....
          Its impossible that never we will find a difference between two primes that cannot be one of that list.
          Ludovicus



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