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Twin Primes

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  • eharsh82
    Hi, similar to the reisel and the Sierpinski problem is there a twin prime conjecture for k such that k is a multiple of 3 and k*2^n+1 | k*2^n-1 can never be
    Message 1 of 17 , Jul 18, 2003
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      Hi,
      similar to the reisel and the Sierpinski problem is there a twin
      prime conjecture for k such that k is a multiple of 3 and

      k*2^n+1 | k*2^n-1 can never be prime for sure.(ie. one of then always
      has a factor)

      I have found twin primes for all numbers less than 3*37=111.

      Thanks!
      Harsh Aggarwal
    • sleephound
      Brier Numbers are values of k that are simultaneously Reisel numbers and Sierpinski Numbers. Several Brier numbers are known. These would clearly be
      Message 2 of 17 , Jul 18, 2003
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        Brier Numbers are values of "k" that are simultaneously Reisel numbers
        and Sierpinski Numbers. Several Brier numbers are known. These would
        clearly be examples of "no twin primes" because there would be no
        primes on either side.


        --- In primenumbers@yahoogroups.com, "eharsh82" <harsh@u...> wrote:
        > Hi,
        > similar to the reisel and the Sierpinski problem is there a twin
        > prime conjecture for k such that k is a multiple of 3 and
        >
        > k*2^n+1 | k*2^n-1 can never be prime for sure.(ie. one of then always
        > has a factor)
        >
        > I have found twin primes for all numbers less than 3*37=111.
        >
        > Thanks!
        > Harsh Aggarwal
      • Jack Brennen
        ... As I posted here last November: http://groups.yahoo.com/group/primenumbers/message/9844 The value k=111 almost certainly yields no twins of the form
        Message 3 of 17 , Jul 18, 2003
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          Harsh wrote:
          > similar to the reisel and the Sierpinski problem is there a twin
          > prime conjecture for k such that k is a multiple of 3 and
          >
          > k*2^n+1 | k*2^n-1 can never be prime for sure.(ie. one of then always
          > has a factor)
          >
          > I have found twin primes for all numbers less than 3*37=111.

          As I posted here last November:

          http://groups.yahoo.com/group/primenumbers/message/9844

          The value k=111 almost certainly yields no twins of the form k*2^n+/-1.

          Proving it seems unlikely.
        • Marty Weissman
          To your knowledge, is there any online list of the first thousand or so sets of twin primes? [Non-text portions of this message have been removed]
          Message 4 of 17 , Feb 13, 2004
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            To your knowledge, is there any online list of the first thousand or so sets of twin primes?


            [Non-text portions of this message have been removed]
          • Sibley
            type twin prime list into google and click on the second link. sibley
            Message 5 of 17 , Feb 13, 2004
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              type "twin prime list" into google and click on the second link.

              sibley

              On Feb 13, 2004, at 2:46 PM, Marty Weissman wrote:

              > To your knowledge, is there any online list of the first thousand or
              > so sets of twin primes?
              >
              >
              > [Non-text portions of this message have been removed]
              >
              >
              >
              > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
              > The Prime Pages : http://www.primepages.org/
              >
              >
              > Yahoo! Groups Links
              >
              >
              >
              >
              >
            • Marty Weissman
              Thanks to all for the help.
              Message 6 of 17 , Feb 13, 2004
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                Thanks to all for the help.
              • bsmath2000
                My real proof of the infinitude of twin primes url had a period at the end because of the sentence it was in, here it is, it should go through this time:
                Message 7 of 17 , Jun 10, 2004
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                  My real proof of the infinitude of twin primes url had a period
                  at the end because of the sentence it was in, here it is, it
                  should go through this time:

                  http://www.lulu.com/bsmath
                • LALGUDI BALASUNDARAM
                  Hi, While I am amazed at the impressive progress made with twin primes, I cannot help feeling some of the basic prime questions for e.g. as to why twin primes
                  Message 8 of 17 , Nov 7, 2004
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                    Hi,
                    While I am amazed at the impressive progress made with
                    twin primes, I cannot help feeling some of the basic
                    prime questions for e.g. as to why twin primes appear
                    only in certain positions in prime sequence and not in
                    other positions remain unanswered (to my knowledge).

                    However much we may pursue with impressive advances in
                    primes, the fact remains prime structure basics will
                    have to be understood to provide the solid foundation
                    for all the impressive advances in primes.

                    I wish to submit my submission on prime structures
                    carries answers to some of these basic questions and
                    look forward to building stronger foundations of prime
                    behaviour based on prime structures.


                    L.J.Balasundaram



                    __________________________________
                    Do you Yahoo!?
                    Check out the new Yahoo! Front Page.
                    www.yahoo.com
                  • Marty Weissman
                    As far as the twin primes we know, is it true that there is a pair between every set of integers between P and P squared, where P is any prime number 2?
                    Message 9 of 17 , Apr 24, 2005
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                      As far as the twin primes we know, is it true that there is a pair between every set of integers between P and P squared, where P is any prime number > 2?


                      [Non-text portions of this message have been removed]
                    • Décio Luiz Gazzoni Filho
                      ... No, try 19. ? forprime(p=19^2,20^2,print(p)) 367 373 379 383 389 397 There s also 53. ? forprime(p=53^2,54^2,print(p)) 2819 2833 2837 2843 2851 2857 2861
                      Message 10 of 17 , Apr 24, 2005
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                        On Sunday 24 April 2005 22:54, you wrote:
                        > As far as the twin primes we know, is it true that there is a pair between
                        > every set of integers between P and P squared, where P is any prime number
                        > > 2?

                        No, try 19.

                        ? forprime(p=19^2,20^2,print(p))
                        367
                        373
                        379
                        383
                        389
                        397

                        There's also 53.

                        ? forprime(p=53^2,54^2,print(p))
                        2819
                        2833
                        2837
                        2843
                        2851
                        2857
                        2861
                        2879
                        2887
                        2897
                        2903
                        2909

                        Nothing else up to 50000, and no other counterexamples are expected. That's
                        because heuristically, twin prime pairs in the vicinity of n occur about
                        every O(log^2 n) integers, and your interval has (n+1)^2 - n^2 = 2n + 1
                        integers. Since 2n + 1 grows faster than log^2 n, one would expect no
                        counterexamples to your statement other than these `small' ones. By the way,
                        numerical evidence using some better approximations (including constants and
                        so on) lends credence to this heuristic.

                        Décio


                        [Non-text portions of this message have been removed]
                      • Jens Kruse Andersen
                        ... You seem to modestly only ask for a twin prime pair between P and P^2. That is satisfied for all numbers 2
                        Message 11 of 17 , Apr 25, 2005
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                          Marty Weissman wrote:

                          > As far as the twin primes we know, is it true that there is a pair between
                          > every set of integers between P and P squared, where P is any prime
                          > number > 2?

                          You seem to modestly only ask for a twin prime pair between P and P^2.
                          That is satisfied for all numbers 2 < P < 33218925*2^169690-1

                          33218925*2^169690+/-1 with 51090 digits is the largest known twin, found by
                          Danial Papp with Proth.exe.
                          For all smaller twins n+/-1, there is a known twin between this and (n-1)^2.

                          --
                          Jens Kruse Andersen
                        • Marty Weissman
                          Thanks to all who replied. ... From: Jens Kruse Andersen To: Sent: Monday, April 25, 2005 7:12 AM
                          Message 12 of 17 , Apr 25, 2005
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                            Thanks to all who replied.
                            ----- Original Message -----
                            From: "Jens Kruse Andersen" <jens.k.a@...>
                            To: <primenumbers@yahoogroups.com>
                            Sent: Monday, April 25, 2005 7:12 AM
                            Subject: Re: [PrimeNumbers] Twin Primes


                            >
                            > Marty Weissman wrote:
                            >
                            >> As far as the twin primes we know, is it true that there is a pair
                            >> between
                            >> every set of integers between P and P squared, where P is any prime
                            >> number > 2?
                            >
                            > You seem to modestly only ask for a twin prime pair between P and P^2.
                            > That is satisfied for all numbers 2 < P < 33218925*2^169690-1
                            >
                            > 33218925*2^169690+/-1 with 51090 digits is the largest known twin, found
                            > by
                            > Danial Papp with Proth.exe.
                            > For all smaller twins n+/-1, there is a known twin between this and
                            > (n-1)^2.
                            >
                            > --
                            > Jens Kruse Andersen
                            >
                            >
                            >
                            >
                            > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
                            > The Prime Pages : http://www.primepages.org/
                            >
                            >
                            > Yahoo! Groups Links
                            >
                            >
                            >
                            >
                            >
                            >
                            >
                            >
                          • Bob Gilson
                            I was trying to discover what I thought should be a simple thing, about primes the other day. Is there a way of calculating, for any PI(x) (within reason),
                            Message 13 of 17 , Jan 7, 2008
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                              I was trying to discover what I thought should be a simple thing, about primes the other day.

                              Is there a way of calculating, for any PI(x) (within reason), what proportion in percentage terms the twin primes play their part?

                              Example: when (x) = 100, the twin primes account for 66.67% of the total primes.

                              Of course, in this example 5 has to be counted twice, - a condition not to be repeated later.

                              As PI(x) gets larger does the percentage of twin primes continue to decline in relation to the total primes, or does it settle down to a constant percentage? Are there any tables available and if so up to what value of PI(x)?

                              Many thanks

                              Bob

                              [Non-text portions of this message have been removed]
                            • Andrey Kulsha
                              ... http://www.ieeta.pt/~tos/primes.html Best, Andrey [Non-text portions of this message have been removed]
                              Message 14 of 17 , Jan 7, 2008
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                                > Are there any tables available and if so up to what value of PI(x)?

                                http://www.ieeta.pt/~tos/primes.html

                                Best,

                                Andrey

                                [Non-text portions of this message have been removed]
                              • Werner D. Sand
                                ... about primes the other day. ... proportion in percentage terms the twin primes play their part? ... total primes. ... not to be repeated later. ... decline
                                Message 15 of 17 , Jan 10, 2008
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                                  --- In primenumbers@yahoogroups.com, Bob Gilson <bobgillson@...>
                                  wrote:
                                  >
                                  > I was trying to discover what I thought should be a simple thing,
                                  about primes the other day.
                                  >
                                  > Is there a way of calculating, for any PI(x) (within reason), what
                                  proportion in percentage terms the twin primes play their part?
                                  >
                                  > Example: when (x) = 100, the twin primes account for 66.67% of the
                                  total primes.
                                  >
                                  > Of course, in this example 5 has to be counted twice, - a condition
                                  not to be repeated later.
                                  >
                                  > As PI(x) gets larger does the percentage of twin primes continue to
                                  decline in relation to the total primes, or does it settle down to a
                                  constant percentage? Are there any tables available and if so up to
                                  what value of PI(x)?
                                  >
                                  > Many thanks
                                  >
                                  > Bob
                                  >
                                  > [Non-text portions of this message have been removed]
                                  >


                                  Hi Bob,

                                  The approximate number of primes <=x is pi(x) ~ x/log x.
                                  The approximate number of twins <=x is pi2(x) ~ x/(log x)².
                                  The quotient of both is log x.

                                  WDS
                                • Kermit Rose
                                  ## between 3 and 3*5; 3 pairs of twin primes; Prime number theorem estimates 0 ## between 3*5 and 3*5*7; 6 pairs of twin primes; Prime number theorem
                                  Message 16 of 17 , Jul 19, 2011
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                                    ## between 3 and 3*5; 3 pairs of twin primes;
                                    Prime number theorem estimates 0

                                    ## between 3*5 and 3*5*7; 6 pairs of twin primes;
                                    Prime number theorem estimates 5

                                    ## between 3*5*7 and 3*5*7*11; 32 pairs of twin primes;
                                    Prime number theorem estimates 18

                                    ## between 3*5*7*11 and 3*5*7*11*13; 231 pairs of twin primes;
                                    Prime number theorem estimates 144

                                    ## between 3*5*7*11*13 and 3*5*7*11*13*17; 2355 pairs of twin primes;
                                    Prime number theorem estimates 1503

                                    ## between 3*5*7*11*13*17 and 3*5*7*11*13*19; 28999 pairs of twin primes;
                                    Prime number theorem estimates 18961

                                    ## between 3*5*7*11*13*19 and 3*5*7*11*13*19*23; Estimated is :
                                    Prime number theorem estimates 305907

                                    For the prime number theorem estimates,
                                    I used the formula

                                    Upper/ ( (ln(upper))**2 - Lower/ ( (ln(lower))**2


                                    I note that the estimates, estimated in this way are significantly lower
                                    than actual.

                                    I presume that someone has figured out a much better formula, still
                                    consistent with the prime number theorem,
                                    for estimating the number of twin primes less than a given integer.

                                    Kermit
                                  • Chris Caldwell
                                    ... http://primes.utm.edu/top20/page.php?id=1
                                    Message 17 of 17 , Jul 19, 2011
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                                      > I presume that someone has figured out a much better formula, still
                                      > consistent with the prime number theorem,
                                      > for estimating the number of twin primes less than a given integer.

                                      http://primes.utm.edu/top20/page.php?id=1
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