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25599Re: Every Prime Number > 5 can be expressed as the sum of . . .

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  • Luis Rodriguez
    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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