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Re: Prime Number Progressions

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  • Mark Underwood
    Hi and welcome to the list! Yes certainly this is the place to share your findings, certainly myself and others would be interested in seeing your work and the
    Message 1 of 3 , Aug 2, 2003
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      Hi and welcome to the list! Yes certainly this is the place to share
      your findings, certainly myself and others would be interested in
      seeing your work and the kind of progressions you are talking of.

      From the Prime Pages, here's a progression that Euler came up with
      over 200 years ago:

      Start with
      41, add 2 = 43
      43, add 4 = 47
      47, add 6 = 53
      53, add 8 = 61
      61, add 10 = 71
      71, add 12 = 83

      and so on for 33 more terms to yield 40 primes! All of which is the
      same as the equation
      x^2 + x + 41 for x=0 to x=39.

      In 1998 Manfred Toplic found ten consecutive primes in arithmetic
      progression:

      P = 100 99697 24697 14247 63778 66555 87969 84032 95093 24689 19004
      18036 03417 75890 43417 03348 88215 90672 29719,

      +210, + 420, + 630, + 840, + 1050, + 1260, + 1470, + 1680 and + 1890.

      I wouldn't doubt if others have found larger by now. I think it was
      Phil Carmody who came up with a big one fairly recently but I don't
      know how big.


      Mark


      --- In primenumbers@yahoogroups.com, ginnyw@a... wrote:
      > I am new to the list and would like to know if others are
      interested in
      > finding progressions of prime numbers. I have written a program
      which searches for
      > the progressions. While the results aren't spectacular, the number
      of
      > progressions found is perhaps new. For example the program found
      54 progressions of
      > 11 primes, 2 progressions of 18 primes, etc. Is this a subject for
      the list,
      > and if it is, would someone be interested in reviewing my work.
      >
      > Thank you.
      >
      > Virginia W.
      >
      >
      > [Non-text portions of this message have been removed]
    • ginnyw@aol.com
      Mark, Thank you for your email. The progressions are the ordinary arithmetic type. One of the progressions of 11 primes is: 17 add 44 = 61 61 add 88
      Message 2 of 3 , Aug 3, 2003
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        Mark,

        Thank you for your email. The progressions are the ordinary arithmetic type.
        One of the progressions of 11 primes is:
        17 add 44 = 61
        61 add 88 = 149
        149 add 132 = 281
        281 add 176 = 457 and continuing for 6 more terms until a nonprime 2921 is
        reached.

        My program uses a constant to search for the progressions. I started with
        pencil and paper and then wrote the program. Except for the progression which
        generates 40 primes, the largest progression I have to date generates 29
        primes. Perhaps that might be a record. Most of the progressions are with small
        numbers because of the limitations of my computer.

        Virginia W.



        [Non-text portions of this message have been removed]
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