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

Re: Lucas super-pseudoprime puzzle

Expand Messages
  • djbroadhurst
    ... More offers of help have come in. So far, these are the volunteers: job=0: David Broadhurst: completed job=1: allocated to David Cleaver job=2: allocated
    Message 1 of 33 , May 26, 2010
    • 0 Attachment
      --- In primenumbers@yahoogroups.com,
      "djbroadhurst" <d.broadhurst@...> wrote:

      > Puzzle: Find the smallest composite integer n > 7056721
      > such that V(a,1,n) = a mod n, for every integer a.

      More offers of help have come in.
      So far, these are the volunteers:

      job=0: David Broadhurst: completed
      job=1: allocated to David Cleaver
      job=2: allocated to Kevin Acres
      job=3: allocated to Mike Oakes
      job=4: allocated to Christ van Willegen
      job=5: allocated to Ray Chandler
      job=6: David Broadhurst: running
      job=7: David Broadhurst: running
      job=8: allocated to David Cleaver

      We are now also testing the range n > 79397009999,
      where there are an infinite number of slots. If you
      would like one of these, please reply off-list.

      With thanks,

      David Broadhurst
    • mikeoakes2
      ... You did very much what I did. I nearly fell off the chair when I averaged everything out and saw 0.57... :-) ... Not very. Would you buy an appeal to
      Message 33 of 33 , May 27, 2010
      • 0 Attachment
        --- In primenumbers@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
        >
        > I tried 1/n^c:
        >
        > v=[1237.1, 328.7, 105.4, 28.01, 6.22 , 1.510, 0.439, 0.0939];
        > print(vector(8,k,-log(v[k]/10^6)/(k+4)/log(10)));
        >
        > [0.5815, 0.5805, 0.5682, 0.5691, 0.5785, 0.5821, 0.5780, 0.5856]
        >
        > and then A/n^c, using the first datum to remove A:
        >
        > print(vector(7,k,-log(v[k+1]/v[1])/k/log(10)));
        >
        > [0.5756, 0.5348, 0.5484, 0.5747, 0.5827, 0.5750, 0.5885]
        >
        > In both cases c =~ Euler looks rather convincing,
        > given the statistics. Well spotted, Sir!

        You did very much what I did.
        I nearly fell off the chair when I averaged everything out and saw 0.57... :-)

        > How strongly are you committed to A = 1, for the average,
        > given the variability of the overall factor with a?

        Not very.
        Would you buy an appeal to Occam's razor, mon vieux?

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