Loading ...
Sorry, an error occurred while loading the content.

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

Expand Messages
  • odj17497
    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,
    Message 1 of 2 , Sep 13, 2007
    • 0 Attachment
      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
    • Johannes Z.
      Hi Gerald, I m not a mathguy, but i would like to show you a different approach, which brings up rather similar findings regarding to multiples of 210,
      Message 2 of 2 , Sep 14, 2007
      • 0 Attachment
        Hi Gerald,

        I m not a mathguy, but i would like to show you a different approach,
        which brings up rather similar findings regarding to multiples of 210,
        surrounded by +/- six prime-candidates.

        Paint on paper a sieve
        (http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes ) with the wide of
        a primorial ( http://en.wikipedia.org/wiki/Primorial ). In your case
        2x3x5x7. Now wipe out only all mulitples of 2, 3 and 5. It will result
        into a sieve with straight lines down. Straight lines down mean, that
        beside that lines you get allways potential primes, which are
        definetly not multiples of 2,3,5. Also it creates a pattern, which you
        can express in multiples of [210 +/-(1,7,11,13,17,19,23,29)] Compare
        it with your findings now.

        I dont know how you came up with your formula, but I think the
        primorial-way is an alternative possibility to get the same in result?

        It should also be possible to have similar findings in other primorial
        ranges. So for example you may find (but it shouldnt be so easy)
        Primes-patterns within Multiples of (2310 +/- (all whats left if you
        wipe out all multiples of 2,3,5,7 within range of 2310)). The problem
        is, as higher as you step on, you will get within that pattern mostly
        only potential primes, which turn out as composits of primes higher
        than for example 2,3,5,7 in the 2310-example later.

        I wounder for some time now, why this connection isnt used regulary in
        computer-searches for great primes, but i guess it has some cpu-reason...

        (Sorry if I got something wrong, someone correct me then, i just like
        the pattern-part of numbers, in general math I got actually pretty bad
        marks in school and with computer science you can hunt me =p)

        Johannes
      Your message has been successfully submitted and would be delivered to recipients shortly.