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1931 4241 6551 8861 11171

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  • Bob Gilson
    A cursory glance at some prime numbers the other day, came up with the following sequence 1931 4241 6551 8861 11171 5 primes in arithmetic progression
    Message 1 of 3 , Jul 7, 2009
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      A cursory glance at some prime numbers the other day, came up with the following sequence

      1931 4241 6551 8861 11171

      5 primes in arithmetic progression separated by 2310. Not very remarkable in itself, except that each of these primes is a twin prime.

      Which leads me to wonder what is the longest known sequence of twin primes in an arithmetic progression?

      Can anyone guide me on this?

      Bob 

      [Non-text portions of this message have been removed]
    • Yann Guidon
      ... well, it does not seem surprising since 2310 is 11# or if you want 11*7*5*3*2. If x+11# has a given gap, there is a good chance that x+(y+11#) has the same
      Message 2 of 3 , Jul 7, 2009
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        Bob Gilson wrote:
        > A cursory glance at some prime numbers the other day, came up with the following sequence
        > 1931 4241 6551 8861 11171
        > 5 primes in arithmetic progression separated by 2310.
        > Not very remarkable in itself, except that each of these primes is a twin prime.

        well, it does not seem surprising since 2310 is 11#
        or if you want 11*7*5*3*2. If x+11# has a given gap, there
        is a good chance that x+(y+11#) has the same gap for some y.
        It's all about wheel sieves ;-)

        > Which leads me to wonder what is the longest known sequence of twin primes in an arithmetic progression?

        If twin primes are infinite (which i don't doubt),
        then there can be arbitrarily long sequences of the above form,
        but with a higher primorial than 11#.

        > Can anyone guide me on this?

        Hope I helped.

        What is interesting to me is how the gap is "closed",
        that is : given a prime p, what is the formulat that
        finds the maximum y where x+(y*p#) becomes composite
        for all the valid x.

        regards,

        > Bob
        yg
      • Jens Kruse Andersen
        ... http://www.primepuzzles.net/puzzles/puzz_121.htm shows: 302296020 + 153363210*n +/- 1, for n=0..9 -- Jens Kruse Andersen
        Message 3 of 3 , Jul 7, 2009
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          Bob Gilson wrote:
          > Which leads me to wonder what is the longest known sequence of twin primes
          > in an arithmetic progression?

          http://www.primepuzzles.net/puzzles/puzz_121.htm shows:
          302296020 + 153363210*n +/- 1, for n=0..9

          --
          Jens Kruse Andersen
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