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RE: [PrimeNumbers] Counting Primes

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  • Chris Caldwell
    Use http://primes.utm.edu/nthprime/ CC ... From: primenumbers@yahoogroups.com [mailto:primenumbers@yahoogroups.com] On Behalf Of Kermit Rose Sent: Tuesday,
    Message 1 of 7 , Aug 17, 2010
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      Use http://primes.utm.edu/nthprime/

      CC


      -----Original Message-----
      From: primenumbers@yahoogroups.com [mailto:primenumbers@yahoogroups.com]
      On Behalf Of Kermit Rose
      Sent: Tuesday, August 17, 2010 10:44 AM
      To: primenumbers@yahoogroups.com
      Subject: [PrimeNumbers] Counting Primes

      Hello Prime Number Friends.

      My recently constructed prime number counting program
      returned the following counts.

      I'm not sure my program is completely debugged.

      Does anyone have the tools to confirm or contradict
      these results?

      # Number primes between 1 and 2 is 1 .
      # Number primes between 2 and 4 is 2 .
      # Number primes between 4 and 8 is 2 .
      # Number primes between 8 and 16 is 2 .
      # Number primes between 16 and 32 is 5 .
      # Number primes between 32 and 64 is 7 .
      # Number primes between 64 and 128 is 13 .
      # Number primes between 128 and 256 is 23 .
      # Number primes between 256 and 512 is 43 .
      # Number primes between 512 and 1024 is 75 .
      # Number primes between 1024 and 2048 is 137 .
      # Number primes between 2048 and 4096 is 255 .
      # Number primes between 4096 and 8192 is 464 .
      # Number primes between 8192 and 16384 is 872 .
      # Number primes between 16384 and 32768 is 1900 .
      # Number primes between 32768 and 65536 is 3512 .
      # Number primes between 65536 and 131072 is 6543 .
      # Number primes between 131072 and 262144 is 12251 .
      # Number primes between 262144 and 524288 is 23000 .
      # Number primes between 524288 and 1048576 is 43390 .
      # Number primes between 1048576 and 2097152 is 82025 .
      # Number primes between 2097152 and 4194304 is 155611 .
      # Number primes between 4194304 and 8388608 is 295947 .
      # Number primes between 8388608 and 16777216 is 564163 .
      # Number primes between 16777216 and 33554432 is 1077871 .
      # Number primes between 33554432 and 67108864 is 2063689 .
      # Number primes between 67108864 and 134217728 is 3957809 .


      Kermit



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    • Ray Chandler
      Or use http://www.research.att.com/~njas/sequences/A036378 which counts primes p such that 2^n
      Message 2 of 7 , Aug 17, 2010
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        Or use http://www.research.att.com/~njas/sequences/A036378 which counts
        primes p such that 2^n<p<=2^(n+1).

        Adjusting for counting 2 in both 1st and 2nd interval, your counts run into
        trouble after 14th term 872.
        Ray


        _____

        From: primenumbers@yahoogroups.com [mailto:primenumbers@yahoogroups.com] On
        Behalf Of Chris Caldwell
        Sent: Tuesday, August 17, 2010 11:40 AM
        To: kermit@...; primenumbers@yahoogroups.com
        Subject: RE: [PrimeNumbers] Counting Primes




        Use http://primes.utm.edu/nthprime/

        CC

        -----Original Message-----
        From: primenumbers@yahoogroups.com <mailto:primenumbers%40yahoogroups.com>
        [mailto:primenumbers@yahoogroups.com <mailto:primenumbers%40yahoogroups.com>
        ]
        On Behalf Of Kermit Rose
        Sent: Tuesday, August 17, 2010 10:44 AM
        To: primenumbers@yahoogroups.com <mailto:primenumbers%40yahoogroups.com>
        Subject: [PrimeNumbers] Counting Primes

        Hello Prime Number Friends.

        My recently constructed prime number counting program
        returned the following counts.

        I'm not sure my program is completely debugged.

        Does anyone have the tools to confirm or contradict
        these results?

        # Number primes between 1 and 2 is 1 .
        # Number primes between 2 and 4 is 2 .
        # Number primes between 4 and 8 is 2 .
        # Number primes between 8 and 16 is 2 .
        # Number primes between 16 and 32 is 5 .
        # Number primes between 32 and 64 is 7 .
        # Number primes between 64 and 128 is 13 .
        # Number primes between 128 and 256 is 23 .
        # Number primes between 256 and 512 is 43 .
        # Number primes between 512 and 1024 is 75 .
        # Number primes between 1024 and 2048 is 137 .
        # Number primes between 2048 and 4096 is 255 .
        # Number primes between 4096 and 8192 is 464 .
        # Number primes between 8192 and 16384 is 872 .
        # Number primes between 16384 and 32768 is 1900 .
        # Number primes between 32768 and 65536 is 3512 .
        # Number primes between 65536 and 131072 is 6543 .
        # Number primes between 131072 and 262144 is 12251 .
        # Number primes between 262144 and 524288 is 23000 .
        # Number primes between 524288 and 1048576 is 43390 .
        # Number primes between 1048576 and 2097152 is 82025 .
        # Number primes between 2097152 and 4194304 is 155611 .
        # Number primes between 4194304 and 8388608 is 295947 .
        # Number primes between 8388608 and 16777216 is 564163 .
        # Number primes between 16777216 and 33554432 is 1077871 .
        # Number primes between 33554432 and 67108864 is 2063689 .
        # Number primes between 67108864 and 134217728 is 3957809 .

        Kermit




        [Non-text portions of this message have been removed]
      • Alan Powell
        Kermit I regret to inform you that Mathematica 5.0 gives: PrimePi[134217728]-PrimePi[67108864]=3645744 a 7.9% discrepancy. Regards Alan Powell From: Chris
        Message 3 of 7 , Aug 17, 2010
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          Kermit

          I regret to inform you that Mathematica 5.0 gives:

          PrimePi[134217728]-PrimePi[67108864]=3645744 a 7.9% discrepancy.

          Regards

          Alan Powell

          From: Chris Caldwell
          Sent: Tuesday, August 17, 2010 12:39 PM
          To: kermit@... ; primenumbers@yahoogroups.com
          Subject: RE: [PrimeNumbers] Counting Primes



          Use http://primes.utm.edu/nthprime/

          CC

          -----Original Message-----
          From: primenumbers@yahoogroups.com [mailto:primenumbers@yahoogroups.com]
          On Behalf Of Kermit Rose
          Sent: Tuesday, August 17, 2010 10:44 AM
          To: primenumbers@yahoogroups.com
          Subject: [PrimeNumbers] Counting Primes

          Hello Prime Number Friends.

          My recently constructed prime number counting program
          returned the following counts.

          I'm not sure my program is completely debugged.

          Does anyone have the tools to confirm or contradict
          these results?

          # Number primes between 1 and 2 is 1 .
          # Number primes between 2 and 4 is 2 .
          # Number primes between 4 and 8 is 2 .
          # Number primes between 8 and 16 is 2 .
          # Number primes between 16 and 32 is 5 .
          # Number primes between 32 and 64 is 7 .
          # Number primes between 64 and 128 is 13 .
          # Number primes between 128 and 256 is 23 .
          # Number primes between 256 and 512 is 43 .
          # Number primes between 512 and 1024 is 75 .
          # Number primes between 1024 and 2048 is 137 .
          # Number primes between 2048 and 4096 is 255 .
          # Number primes between 4096 and 8192 is 464 .
          # Number primes between 8192 and 16384 is 872 .
          # Number primes between 16384 and 32768 is 1900 .
          # Number primes between 32768 and 65536 is 3512 .
          # Number primes between 65536 and 131072 is 6543 .
          # Number primes between 131072 and 262144 is 12251 .
          # Number primes between 262144 and 524288 is 23000 .
          # Number primes between 524288 and 1048576 is 43390 .
          # Number primes between 1048576 and 2097152 is 82025 .
          # Number primes between 2097152 and 4194304 is 155611 .
          # Number primes between 4194304 and 8388608 is 295947 .
          # Number primes between 8388608 and 16777216 is 564163 .
          # Number primes between 16777216 and 33554432 is 1077871 .
          # Number primes between 33554432 and 67108864 is 2063689 .
          # Number primes between 67108864 and 134217728 is 3957809 .

          Kermit

          ------------------------------------

          Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
          The Prime Pages : http://www.primepages.org/

          Yahoo! Groups Links





          [Non-text portions of this message have been removed]
        • Kermit Rose
          ... Thank you Ray and Chris. I have corrected the bugs in my program that led to those particular incorrect counts. It now counts correctly the primes between
          Message 4 of 7 , Aug 17, 2010
          • 0 Attachment
            On 8/17/2010 1:03 PM, Ray Chandler wrote:
            > Or use http://www.research.att.com/~njas/sequences/A036378 which counts
            > primes p such that 2^n<p<=2^(n+1).
            > Adjusting for counting 2 in both 1st and 2nd interval, your counts run
            > into trouble after 14th term 872.
            > Ray
            >

            Thank you Ray and Chris.

            I have corrected the bugs in my program that led to
            those particular incorrect counts.

            It now counts correctly the primes between consecutive powers
            of two, up to the time constraint limits of running the program.

            Kermit
          • elevensmooth
            ... nthprime says the number of primes below 67108864 is 3957809 A remarkable coincidence that suggests a cut and paste error someplace.
            Message 5 of 7 , Aug 18, 2010
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              --- In primenumbers@yahoogroups.com, "Chris Caldwell" <caldwell@...> wrote:
              >
              > Use http://primes.utm.edu/nthprime/
              >

              >> # Number primes between 67108864 and 134217728 is 3957809

              nthprime says the number of primes below 67108864 is 3957809

              A remarkable coincidence that suggests a cut and paste error someplace.
            • Matteo Mattsteel Vitturi
              Hello Kermit :-) Using my old MathCAD 4.0 I ve found that the discrepance begins at # Number primes between 16384 and 32768 is 1900 . It should be (it is)
              Message 6 of 7 , Aug 18, 2010
              • 0 Attachment
                Hello Kermit :-)
                Using my old MathCAD 4.0 I've found that the discrepance begins at # Number primes between 16384 and 32768 is 1900 .
                It should be (it is) 1612.
                Following discrepancies are increasingly larger.
                Regards
                Matteo.

                To: primenumbers@yahoogroups.com
                From: kermit@...
                Date: Tue, 17 Aug 2010 11:44:26 -0400
                Subject: [PrimeNumbers] Counting Primes




























                Hello Prime Number Friends.



                My recently constructed prime number counting program

                returned the following counts.



                I'm not sure my program is completely debugged.



                Does anyone have the tools to confirm or contradict

                these results?



                # Number primes between 1 and 2 is 1 .

                # Number primes between 2 and 4 is 2 .

                # Number primes between 4 and 8 is 2 .

                # Number primes between 8 and 16 is 2 .

                # Number primes between 16 and 32 is 5 .

                # Number primes between 32 and 64 is 7 .

                # Number primes between 64 and 128 is 13 .

                # Number primes between 128 and 256 is 23 .

                # Number primes between 256 and 512 is 43 .

                # Number primes between 512 and 1024 is 75 .

                # Number primes between 1024 and 2048 is 137 .

                # Number primes between 2048 and 4096 is 255 .

                # Number primes between 4096 and 8192 is 464 .

                # Number primes between 8192 and 16384 is 872 .

                # Number primes between 16384 and 32768 is 1900 .

                # Number primes between 32768 and 65536 is 3512 .

                # Number primes between 65536 and 131072 is 6543 .

                # Number primes between 131072 and 262144 is 12251 .

                # Number primes between 262144 and 524288 is 23000 .

                # Number primes between 524288 and 1048576 is 43390 .

                # Number primes between 1048576 and 2097152 is 82025 .

                # Number primes between 2097152 and 4194304 is 155611 .

                # Number primes between 4194304 and 8388608 is 295947 .

                # Number primes between 8388608 and 16777216 is 564163 .

                # Number primes between 16777216 and 33554432 is 1077871 .

                # Number primes between 33554432 and 67108864 is 2063689 .

                # Number primes between 67108864 and 134217728 is 3957809 .



                Kermit



















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