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

Re: [PrimeNumbers] Re: Prime chains x-->Ax+B [puzzle 2]

Expand Messages
  • Kevin Acres
    Hello David, ... Thanks for that. It will give me some idea of what to hope for at least. Right now I m trawling shallow waters again. This gives me faster
    Message 1 of 143 , Jan 2, 2011
    • 0 Attachment
      Hello David,

      At 09:43 AM 3/01/2011, djbroadhurst wrote:
      >--- In primenumbers@yahoogroups.com, Kevin Acres <research@...> wrote:
      > > after now having found 17 15/16 chains, should
      > > I reasonably be expecting a 16/16 some time soon?
      >
      >Suppose that you guessed a 1/9 chance. Then the odds
      >of /not/ getting a result after 17 tries are
      >exp(-17/9) =~ 15%

      Thanks for that. It will give me some idea of what to hope for at least.

      Right now I'm trawling shallow waters again. This gives me faster
      processing and a greater 15/16 density. Over the next couple of days
      I'm going to take b up to just less than 2^31 with x < 51561510. I
      expect this to give an extra 6 or so 15/16 chains on top of the 18 I have now.

      The current state of my search is:

      0 < b < 506306000, 0 < x < 511020510 -> completed
      506306000 < b < 1000479680, 0 < x < 51561510 -> completed
      1000479680 < b < 1600328930, 0 < x < 51561510 -> 50% complete (~17
      hours to go)
      1600328930 < b < 2147085140, 0 < x < 51561510 -> not yet started (~32 hours)

      For completeness, my 18th 15/16 is:

      [18*x + 1220760325, [38738527, 15]]


      Best Regards,

      Kevin.
    • djbroadhurst
      ... Suppose that we want to start with a square and get a square. Then we must solve the Diophantine equation y^2 = a*x^2 + b For any pair (a,b), Dario will
      Message 143 of 143 , Jan 7, 2011
      • 0 Attachment
        --- In primenumbers@yahoogroups.com,
        Kevin Acres <research@...> wrote:

        > x=a*x+b either is a square or has a square as a major factor.

        Suppose that we want to start with a square and get a square.
        Then we must solve the Diophantine equation
        y^2 = a*x^2 + b

        For any pair (a,b), Dario will tell us all the solutions:
        http://www.alpertron.com.ar/QUAD.HTM

        David
      Your message has been successfully submitted and would be delivered to recipients shortly.