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19084((A)-(A^2)+1)*(13))*(A)*((A)+(A^2)+1)*(13))=B, fits a model

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  • odj17497
    Sep 13, 2007
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      To all interested:

      Sometimes there's a multiple of 210 that's symmetrically surrounded
      by twelve primes, six on both sides, by distances of 1, 11, 13, 17,
      19, and 23. It's referred to as a prime galaxy center. An example
      appears below:

      41,280,160,361,347

      41,280,160,361,351

      41,280,160,361,353

      41,280,160,361,357

      41,280,160,361,359

      41,280,160,361,369
      -> 41,280,160,361,370, the center
      41,280,160,361,371

      41,280,160,361,381

      41,280,160,361,383

      41,280,160,361,387

      41,280,160,361,389

      41,280,160,361,393

      There may be a way to obtain (not this very one but) sequences like
      this by this formula:

      First obtain an A that fits certain congruence class criteria (will
      be shown later). Then subtract the same quantity from it as you add
      to it, multiplying the three factors together:

      ((A)-((A^2)+1)*(13))*(A)*((A)+((A^2)+1)*(13))=B, B fitting some
      proper subset for the general prime galaxy model.

      If B is squarefree, then A is congruent to:

      2(4)

      3(9)

      Squarefreely 0(5)

      Squarefreely 0(7), or else 2(7) not congruent to 5(49), or 3(7)
      not congruent to 10(49)

      3(11)

      2, 5, or 6(13)

      7(17)

      9(19)

      5(23)

      Squarefreely 0 or else 14(29), etc.

      Would anyone want to search for primes using this method?

      Owen Jarand
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