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[PrimeNumbers] RE:prime number frequencies

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  • mikeoakes2@aol.com
    ... From my NMBRTHRY post http://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0403&L=NMBRTHRY&P=R1117&I=-3 here is another data point for your table: x 1
    Message 1 of 5 , Nov 30, 2005
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      In an email dated Mon, 28 11 2005 2:19:43 pm GMT, "newjack56" <mrnsigepalum@...> writes:

      >As a follow up to my earlier post on prime frequencies (sorry, don't
      >have it with me at the momoment) I was trying to find a way in
      >determining n as prime with it ending either in 1, 3, 7, or 9. Chris
      >pointed me into a direction on the internet (thank you) and I found
      >some amazing results. I found this table from a project Andrew
      >Granville and Greg Martin worked on.
      >
      >x                  1         3          7           9
      >100                5         7          6           7
      >200                10        12         12          10
      >500                22        24         24          23
      >.
      >.
      >.
      >500,000          10,386     10,382    10,403      10,365
      >1,000,000        19,617     19,665    19,621      19,593
      >
      >The lead trades off between 3 and 7. Also, the number of primes of x
      >following the formula 3n+2 had the strongest and most dominate course.


      From my NMBRTHRY post
      http://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0403&L=NMBRTHRY&P=R1117&I=-3

      here is another data point for your table:

      x 1 3 7 9
      10^13 86516370000 86516427946 86516367790 86516371101

      where 3 is in the lead, but only by an incredibly small relative margin.

      This is line with theory, which says that asymptotically the 4 fractions are equal.

      So I don't think anything useful can come out of this line of investigation.

      -Mike Oakes
    • grostoon
      ... Sure, and x=2 is also required ... J-L
      Message 2 of 5 , Dec 1, 2005
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        --- In primenumbers@yahoogroups.com, Alan Eliasen <eliasen@m...> wrote:

        > In order for x^n-1 to be prime, n must be prime.
        >

        Sure, and x=2 is also required ...


        J-L
      • pbtoau
        118751673=3*997*39703
        Message 3 of 5 , Dec 8, 2005
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          118751673=3*997*39703
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