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

Prime Number Progressions

Expand Messages
  • ginnyw@aol.com
    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
    Message 1 of 3 , Aug 2, 2003
    • 0 Attachment
      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]
    • 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 2 of 3 , Aug 2, 2003
      • 0 Attachment
        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 3 of 3 , Aug 3, 2003
        • 0 Attachment
          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]
        Your message has been successfully submitted and would be delivered to recipients shortly.