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Re: [PrimeNumbers] Re: Enough

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  • Andy Steward
    ... I have RPB s file plus my own discoveries. Here goes. 926,663 prime factors of GRUs, at least 5 digits, first digit: d Count Prop Benford 1 291554
    Message 1 of 5 , Dec 12, 2001
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      David wrote:

      > But I don't have the perl skills to turn Richard's 5MB file
      > into a test, sorry.

      I have RPB's file plus my own discoveries. Here goes.

      926,663 prime factors of GRUs, at least 5 digits, first digit:

      d Count Prop Benford
      1 291554 0.315 0.301
      2 165388 0.178 0.176
      3 115234 0.124 0.125
      4 87749 0.095 0.097
      5 71989 0.078 0.079
      6 59433 0.064 0.067
      7 50697 0.055 0.058
      8 44610 0.048 0.051
      9 40009 0.043 0.046

      Second digit:
      d Count Prop
      0 111386 0.120
      1 106782 0.115
      2 101980 0.110
      3 97322 0.105
      4 92176 0.099
      5 89854 0.097
      6 85939 0.093
      7 83585 0.090
      8 79475 0.086
      9 78164 0.084

      Andy
    • djbroadhurst
      Andy Steward wrote ... Thanks, Andy. My personal opinion is that the slight overpopulation of leading=1 is due to the floor at a power of 10 (here 10^4, in
      Message 2 of 5 , Dec 12, 2001
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        Andy Steward wrote

        > 926,663 prime factors of GRUs, at least 5 digits, first digit:

        > d Count Prop Benford
        > 1 291554 0.315 0.301
        > 2 165388 0.178 0.176
        > 3 115234 0.124 0.125
        > 4 87749 0.095 0.097
        > 5 71989 0.078 0.079
        > 6 59433 0.064 0.067
        > 7 50697 0.055 0.058
        > 8 44610 0.048 0.051
        > 9 40009 0.043 0.046

        Thanks, Andy. My personal opinion is that the slight
        overpopulation of leading=1 is due to the floor at a power
        of 10 (here 10^4, in Brent 10^10). But, as past messages
        have indicated, you always run the risk of
        distorting the distribution in some base,
        by some such selection criterion.

        The good point is that the base-independence of primality
        and the base-independence (one assumes!) of ECM strike-rates
        then unbiases the remainder of the generation procedure.

        And as it's a theorem that

        base-indepedence==>Benford

        we see a reasonable fit.

        Nice work, thanks!

        David
      • Jud McCranie
        ... But the reason that it is near Benford is due to they were obtained from factoring another set of numbers, and thus isn t typical.
        Message 3 of 5 , Dec 12, 2001
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          At 06:10 PM 12/12/2001 +0000, djbroadhurst wrote:

          > Thanks, Andy. My personal opinion is that the slight
          >overpopulation of leading=1 is due to the floor at a power
          >of 10 (here 10^4, in Brent 10^10). But, as past messages
          >have indicated, you always run the risk of
          >distorting the distribution in some base,
          >by some such selection criterion.

          But the reason that it is near Benford is due to they were obtained from
          factoring another set of numbers, and thus isn't typical.


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