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Re: [PrimeNumbers] Prime Game

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  • Kermit Rose
    From: Werner D. Sand Date: 01/02/06 09:30:35 To: primenumbers@yahoogroups.com Subject: [PrimeNumbers] Prime Game 7,31,109,349,1061,103,29,97,43,13 11,41,131,37
    Message 1 of 4 , Jan 2, 2006
      From: Werner D. Sand
      Date: 01/02/06 09:30:35
      To: primenumbers@yahoogroups.com
      Subject: [PrimeNumbers] Prime Game

      7,31,109,349,1061,103,29,97,43,13
      11,41,131,37
      17,59

      If you sum 3 consecutive odd prime numbers p,q,r, you get a number s
      which is either prime or not: p+q+r=s. If s is prime, you call it p
      and repeat the game. If s is not prime, you call the greatest prime
      factor p and repeat the game. Finally, you get into an infinite
      cycle, which is one of the above 3 series, no matter what prime
      numbers you choose. Example: p=7

      7+11+13=31
      31+37+41=109
      109+113+127=349
      349+353+359=1061
      1061+1063+1069=3193=31*103
      103+107+109=319=11*29
      29+31+37=97
      97+101+103=301=7*43
      43+47+53=143=11*13
      13+17+19=49=7*7
      7+11+13…

      Questions:

      1.) Why doesn't the series diverge? Proof?


      Kermit says:

      I started with 113. How far would I have to go to end up with one of the
      3 series?

      I suspect that the termination into one of those three series has something
      to
      do with every prime >3 being of the form 6N+1 or 6N-1.

      [Non-text portions of this message have been removed]
    • Werner D. Sand
      Hi Kermit, after 3 steps you are in the 2nd cycle: 113+127+131=371=7*53 53+59+61=173 173+179+181=533=13*41 41... Werner
      Message 2 of 4 , Jan 3, 2006
        Hi Kermit,

        after 3 steps you are in the 2nd cycle:

        113+127+131=371=7*53
        53+59+61=173
        173+179+181=533=13*41
        41...

        Werner
      • Werner D. Sand
        Guys, I call it a game , but it s mathematics!
        Message 3 of 4 , Jan 4, 2006
          Guys, I call it a "game", but it's mathematics!
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