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Significance of individual digits in prime likeliness...

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  • mgmutch
    5 0 1 0 0 0 0 0 0 0 2 5 0 0 1 0 0 0
    Message 1 of 3 , Jul 30, 2013
      5 0 1 0 0 0 0 0
      0 0 2

      5 0 0 1 0 0 0 0
      0 0 3

      5 0 0 0 0 1 0 0
      0 0 5

      5 0 0 0 0 0 0 1
      0 0 7

      4 2 0 0 0 0 0 0
      0 0 11

      4 2 0 0 0 0 0 0
      0 0 101

      4 1 0 1 0 0 0 0
      0 0 31

      4 1 0 1 0 0 0 0
      0 0 3001

      4 1 0 1 0 0 0 0
      0 0 13

      4 1 0 1 0 0 0 0
      0 0 103

      4 1 0 1 0 0 0 0
      0 0 100003

      4 1 0 0 1 0 0 0
      0 0 41

      4 1 0 0 1 0 0 0
      0 0 401

      4 1 0 0 1 0 0 0
      0 0 4001

      4 1 0 0 0 0 1 0
      0 0 61

      4 1 0 0 0 0 1 0
      0 0 601

      4 1 0 0 0 0 0 1
      0 0 71

      4 1 0 0 0 0 0 1
      0 0 701

      4 1 0 0 0 0 0 1
      0 0 7001

      4 1 0 0 0 0 0 1
      0 0 70001

      4 1 0 0 0 0 0 1
      0 0 700001

      4 1 0 0 0 0 0 1
      0 0 17

      4 1 0 0 0 0 0 1
      0 0 107

      4 1 0 0 0 0 0 1
      0 0 10007

      4 1 0 0 0 0 0 0
      0 1 9001

      4 1 0 0 0 0 0 0
      0 1 90001

      4 1 0 0 0 0 0 0
      0 1 900001

      4 1 0 0 0 0 0 0
      0 1 19

      4 1 0 0 0 0 0 0
      0 1 109

      4 1 0 0 0 0 0 0
      0 1 1009

      4 1 0 0 0 0 0 0
      0 1 10009

      4 0 1 1 0 0 0 0
      0 0 23

      4 0 1 1 0 0 0 0
      0 0 2003

      4 0 1 1 0 0 0 0
      0 0 200003

      4 0 1 0 0 0 0 0
      0 1 29

      4 0 1 0 0 0 0 0
      0 1 200009

      4 0 0 1 1 0 0 0
      0 0 43

      4 0 0 1 1 0 0 0
      0 0 4003

      4 0 0 1 0 1 0 0
      0 0 53

      4 0 0 1 0 1 0 0
      0 0 503

      4 0 0 1 0 1 0 0
      0 0 5003

      4 0 0 1 0 0 0 1
      0 0 73

      4 0 0 1 0 0 0 1
      0 0 70003

      4 0 0 1 0 0 0 1
      0 0 37

      4 0 0 1 0 0 0 1
      0 0 307

      4 0 0 1 0 0 0 1
      0 0 300007

      4 0 0 1 0 0 0 0
      1 0 83

      4 0 0 0 1 0 0 1
      0 0 47

      4 0 0 0 1 0 0 1
      0 0 4007

      4 0 0 0 1 0 0 0
      0 1 409

      4 0 0 0 1 0 0 0
      0 1 40009

      4 0 0 0 1 0 0 0
      0 1 400009

      4 0 0 0 0 1 0 0
      0 1 59

      4 0 0 0 0 1 0 0
      0 1 509

      4 0 0 0 0 1 0 0
      0 1 5009

      4 0 0 0 0 1 0 0
      0 1 500009

      4 0 0 0 0 0 1 1
      0 0 67

      4 0 0 0 0 0 1 1
      0 0 607

      4 0 0 0 0 0 1 1
      0 0 6007

      4 0 0 0 0 0 0 1
      0 1 97

      4 0 0 0 0 0 0 1
      0 1 907

      4 0 0 0 0 0 0 1
      0 1 9007

      4 0 0 0 0 0 0 1
      0 1 90007

      4 0 0 0 0 0 0 1
      0 1 900007

      4 0 0 0 0 0 0 1
      0 1 79

      4 0 0 0 0 0 0 1
      0 1 709

      4 0 0 0 0 0 0 1
      0 1 70009

      4 0 0 0 0 0 0 0
      1 1 89

      4 0 0 0 0 0 0 0
      1 1 809

      4 0 0 0 0 0 0 0
      1 1 8009

      3 2 1 0 0 0 0 0
      0 0 211

      3 2 1 0 0 0 0 0
      0 0 21001

      3 2 1 0 0 0 0 0
      0 0 2011

      3 2 1 0 0 0 0 0
      0 0 20101

      3 2 1 0 0 0 0 0
      0 0 20011

      3 2 1 0 0 0 0 0
      0 0 1201

      3 2 1 0 0 0 0 0
      0 0 1021

      3 2 1 0 0 0 0 0
      0 0 102001

      3 2 0 1 0 0 0 0
      0 0 311

      3 2 0 1 0 0 0 0
      0 0 3011

      3 2 0 1 0 0 0 0
      0 0 30011

      3 2 0 1 0 0 0 0
      0 0 131

      3 2 0 1 0 0 0 0
      0 0 1301

      3 2 0 1 0 0 0 0
      0 0 13001

      3 2 0 1 0 0 0 0
      0 0 113

      3 2 0 1 0 0 0 0
      0 0 1103

      3 2 0 1 0 0 0 0
      0 0 11003

      3 2 0 1 0 0 0 0
      0 0 1031

      3 2 0 1 0 0 0 0
      0 0 10301

      3 2 0 1 0 0 0 0
      0 0 103001

      3 2 0 1 0 0 0 0
      0 0 1013

      3 2 0 1 0 0 0 0
      0 0 10103

      3 2 0 1 0 0 0 0
      0 0 100103




      Any comments?




      [Non-text portions of this message have been removed]
    • Phil Carmody
      On Wed, 7/31/13, mgmutch wrote: [SNIP enormous table with apparently 11 columns, and no meaning] ... Yes - why did I approve that message
      Message 2 of 3 , Jul 31, 2013
        On Wed, 7/31/13, mgmutch <mgmutch@...> wrote:

        [SNIP enormous table with apparently 11 columns, and no meaning]

        > Any comments?

        Yes - why did I approve that message in that form, i.e. with no explanation?

        I don't know if yahoogroups was to blame for the table to be badly formatted (lines split), or whether it's your outgoing mail client, or even my mail reader (also yahoo, spit!), but if it looked badly line wrapped to you too, then consider using a different mail client, your current one isn't sending what you're writing.

        What would be most useful and compact would be an explanation and additionally perhaps a short program used to generate the table. Preferably in Pari/GP, Mathematica, Sage, Maxima, or similar.
        Just a big table of numbers tells us very little.

        Phil
        --
        () ASCII ribbon campaign () Hopeless ribbon campaign
        /\ against HTML mail /\ against gratuitous bloodshed

        [stolen with permission from Daniel B. Cristofani]
      • Jens Kruse Andersen
        ... It looks a little better at http://tech.groups.yahoo.com/group/primenumbers/message/25322 than in the mail. It s still cryptic without an explanation but I
        Message 3 of 3 , Jul 31, 2013
          mgmutch wrote:
          > 4 1 0 1 0 0 0 0
          > 0 0 3001

          It looks a little better at
          http://tech.groups.yahoo.com/group/primenumbers/message/25322
          than in the mail. It's still cryptic without an explanation but I figured
          out what it shows. I didn't figure out any significance though.

          The count of each digit in a prime is given. It assumes 6-digit
          primes with leading 0's allowed and counted, but not written.

          "4 1 0 1 0 0 0 0 0 0 3001" means the prime 3001 has 4 '0'
          (when written as 003001 with 6 digits), 1 '1', 0 '2', 1 '3', 0 '4',
          0 '5', 0 '6', 0 '7', 0 '8', 0 '9'.

          For unknown reasons, the primes appear to be sorted in reverse
          lexicographical order of their digit counts. Primes with the same
          digit count like {31, 3001, 13, 103, 100003} are also sorted
          internally in reverse lexicographical order (without assuming
          leading 0's in the sorting).

          --
          Jens Kruse Andersen
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