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

puzzle: what is special about these 10 consecutive primes?

Expand Messages
  • Mark
    Puzzle: What is special about these 10 consecutive primes? 5981567 5981579 5981609 5981629 5981641 5981659 5981663 5981669 5981681 5981683 Mark
    Message 1 of 6 , Jul 22, 2012
    • 0 Attachment
      Puzzle: What is special about these 10 consecutive primes?

      5981567
      5981579
      5981609
      5981629
      5981641
      5981659
      5981663
      5981669
      5981681
      5981683


      Mark
    • bobgillson@yahoo.com
      I don t know. So what is so special about your 10 sequential prime numbers? Sent from my iPad ... [Non-text portions of this message have been removed]
      Message 2 of 6 , Jul 22, 2012
      • 0 Attachment
        I don't know. So what is so special about your 10 sequential prime numbers?

        Sent from my iPad

        On 22 Jul 2012, at 15:54, "Mark" <mark.underwood@...> wrote:

        >
        > Puzzle: What is special about these 10 consecutive primes?
        >
        > 5981567
        > 5981579
        > 5981609
        > 5981629
        > 5981641
        > 5981659
        > 5981663
        > 5981669
        > 5981681
        > 5981683
        >
        > Mark
        >
        >
        >
        >
        >
        >
        >

        [Non-text portions of this message have been removed]
      • Jens Kruse Andersen
        ... Solved within a minute by searching the first term in OEIS: http://oeis.org/A214219 That may seem like cheating but this property looks difficult to guess.
        Message 3 of 6 , Jul 22, 2012
        • 0 Attachment
          Mark wrote:
          > Puzzle: What is special about these 10 consecutive primes?
          >
          > 5981567
          > 5981579
          > 5981609
          > ...
          > 5981683

          Solved within a minute by searching the first term in OEIS:
          http://oeis.org/A214219
          That may seem like cheating but this property looks difficult to guess.

          So for each k from 1 to 10, k divides the sum of the
          k consecutive primes starting at 5981567:
          1 divides 5981567
          2 divides 5981567 + 5981579
          3 divides 5981567 + 5981579 + 5981609
          ...
          10 divides 5981567 + ... + 5981683.

          A214219 and http://www.primepuzzles.net/puzzles/puzz_415.htm
          also give two more terms:
          148871869 for k = 1 to 11, and 5545986967 for k = 1 to 12.
          My computation agrees and shows 28511128379 for k = 1 to 13,
          and 85185688439 for k = 1 to 14.

          --
          Jens Kruse Andersen
        • Mark
          Bingo! Yes with fresh eyes I see that the puzzle was rather obscure. Should have given a hint. But golly, is there anything that OEIS doesn t have? Good
          Message 4 of 6 , Jul 22, 2012
          • 0 Attachment
            Bingo! Yes with fresh eyes I see that the puzzle was rather obscure. Should have given a hint. But golly, is there anything that OEIS doesn't have? Good find. Jens how you got up to 14 so quickly is beyond me (as usual!).

            The investigation started out innocently enough, as I wanted to know when 2+3+5+7+... would first yield an average number that was an integer (other than 2!). As it turns out one must get to the 23rd prime, 83, for the average to come out to an integer (38). Then one must sum all the primes up to 241 to get the next integer average (110), and then up to the prime 6599 to get the next integer average (3066).

            This is a very low yield compared to starting at other primes, at least most other primes anyways. I would expect the yield to be about half as much as average, but it seems less.


            Mark


            --- In primenumbers@yahoogroups.com, "Jens Kruse Andersen" <jens.k.a@...> wrote:
            >
            > Mark wrote:
            > > Puzzle: What is special about these 10 consecutive primes?
            > >
            > > 5981567
            > > 5981579
            > > 5981609
            > > ...
            > > 5981683
            >
            > Solved within a minute by searching the first term in OEIS:
            > http://oeis.org/A214219
            > That may seem like cheating but this property looks difficult to guess.
            >
            > So for each k from 1 to 10, k divides the sum of the
            > k consecutive primes starting at 5981567:
            > 1 divides 5981567
            > 2 divides 5981567 + 5981579
            > 3 divides 5981567 + 5981579 + 5981609
            > ...
            > 10 divides 5981567 + ... + 5981683.
            >
            > A214219 and http://www.primepuzzles.net/puzzles/puzz_415.htm
            > also give two more terms:
            > 148871869 for k = 1 to 11, and 5545986967 for k = 1 to 12.
            > My computation agrees and shows 28511128379 for k = 1 to 13,
            > and 85185688439 for k = 1 to 14.
            >
            > --
            > Jens Kruse Andersen
            >
          • Walter Nissen
            Nice . Those interested in this puzzle , or even if not , may be interested in Doric Columns of Primes , http://upforthecount.com/math/pdor.html There are some
            Message 5 of 6 , Jul 22, 2012
            • 0 Attachment
              Nice .

              Those interested in this puzzle , or even if not , may be
              interested in Doric Columns of Primes ,
              http://upforthecount.com/math/pdor.html
              There are some "columns" there , some questions and a
              brief description of programming which produced massive
              overlap between integer and floating-point processor
              utilization .

              Cheers ,

              Walter
            • Jens Kruse Andersen
              ... Your text was written in 1991. http://www.primepuzzles.net/puzzles/puzz_181.htm from 2003 has the same 11 terms up to 3163427380990800 and adds 3 more
              Message 6 of 6 , Jul 23, 2012
              • 0 Attachment
                Walter Nissen wrote:
                > Those interested in this puzzle , or even if not , may be
                > interested in Doric Columns of Primes ,
                > http://upforthecount.com/math/pdor.html

                Your text was written in 1991.
                http://www.primepuzzles.net/puzzles/puzz_181.htm from 2003 has the
                same 11 terms up to 3163427380990800 and adds 3 more terms:
                12 22755817971366480 Phil Carmody
                13 3788978012188649280 " "
                14 2918756139031688155200 J. K. Andersen (20/4/03)

                The puzzle asks:
                1) Do you know if this sequence has been studied and published
                before and where?

                You have the answer for that!

                --
                Jens Kruse Andersen
              Your message has been successfully submitted and would be delivered to recipients shortly.