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Prime GAP of 82794

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  • Milton Brown
    There are no prime numbers between 10^5020+47311 and 10^5020-35483 yielding a prime GAP of 82794 (or 82795). These end-points may be (?) certifiable with Primo
    Message 1 of 14 , Sep 29, 2001
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      There are no prime numbers between

      10^5020+47311

      and

      10^5020-35483

      yielding a prime GAP of 82794 (or 82795).

      These end-points may be (?) certifiable
      with Primo 1.0. It is hard to tell with so much
      hype about it. Anyone who cares to try with
      a fast machine for a month or twelve is welcome.

      Milton L. Brown
      miltbrown@...



      [Non-text portions of this message have been removed]
    • Paul Leyland
      ... I make 82794/ln(10^5020+47311) about 7.163. Well short of the 10.0 needed to get on my top-20 page. The latter, BTW, is now under construction and I hope
      Message 2 of 14 , Sep 30, 2001
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        > There are no prime numbers between
        >
        > 10^5020+47311
        >
        > and
        >
        > 10^5020-35483
        >
        > yielding a prime GAP of 82794 (or 82795).

        I make 82794/ln(10^5020+47311) about 7.163.

        Well short of the 10.0 needed to get on my top-20 page. The latter,
        BTW, is now under construction and I hope to make it public within a day
        or two.

        Paul
      • Milton Brown
        Your database seems to be deficient, and its not even published. I think I will make my own. ... From: Paul Leyland To: Milton
        Message 3 of 14 , Sep 30, 2001
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          Your database seems to be deficient, and its
          not even published. I think I will make my own.


          ----- Original Message -----
          From: "Paul Leyland" <pleyland@...>
          To: "Milton Brown" <miltbrown@...>; <primenumbers@yahoogroups.com>
          Sent: Sunday, September 30, 2001 2:00 AM
          Subject: RE: [PrimeNumbers] Prime GAP of 82794



          > There are no prime numbers between
          >
          > 10^5020+47311
          >
          > and
          >
          > 10^5020-35483
          >
          > yielding a prime GAP of 82794 (or 82795).

          I make 82794/ln(10^5020+47311) about 7.163.

          Well short of the 10.0 needed to get on my top-20 page. The latter,
          BTW, is now under construction and I hope to make it public within a day
          or two.

          Paul
        • jfoug@kdsi.net
          Why is it deficient Milton? Because this example does not fit? Well there is not that much special about your find. Yes, it is outside of the normal bounds
          Message 4 of 14 , Sep 30, 2001
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            Why is it "deficient" Milton? Because this example does not fit?
            Well there is not that much special about your find. Yes, it is
            outside of the normal bounds a little, but not too far outside those
            bounds for numbers as large as you are working with. For a pair of
            numbers this size, you need a gap of over 115000 to qualify for Pauls
            list. I see nothing wrong with that, your numbers simply are not
            special enough. You will probably have a hard time finding gaps
            which work if ALL you do is search 10^n-k to 10^n+j. A search like
            you are doing is no better than simply starting at 10^n+1 and
            proceeding forward to 10^n+3, 10^n+5, ... until you find a gap of
            sufficient size. This is a very slow method of search, and for you
            to limit yourself to 10^n-k to 10^n+j you have doomed yourself to this
            method. The method I described in earlier emails can speed up this
            searc by a factor of (D-1) and with D being 10 or more, that means
            that you can search up to 9 times faster.

            --- In primenumbers@y..., "Milton Brown" <miltbrown@e...> wrote:
            >
            > Your database seems to be deficient, and its
            > not even published. I think I will make my own.
            >
            >
            > ----- Original Message -----
            > From: "Paul Leyland" <pleyland@m...>
            > To: "Milton Brown" <miltbrown@e...>; <primenumbers@y...>
            > Sent: Sunday, September 30, 2001 2:00 AM
            > Subject: RE: [PrimeNumbers] Prime GAP of 82794
            >
            >
            >
            > > There are no prime numbers between
            > >
            > > 10^5020+47311
            > >
            > > and
            > >
            > > 10^5020-35483
            > >
            > > yielding a prime GAP of 82794 (or 82795).
            >
            > I make 82794/ln(10^5020+47311) about 7.163.
            >
            > Well short of the 10.0 needed to get on my top-20 page. The latter,
            > BTW, is now under construction and I hope to make it public within
            a day
            > or two.
            >
            > Paul
          • Milton Brown
            Do I understand correctlythat you object to my keeping my own database and making it available? ... From: To:
            Message 5 of 14 , Sep 30, 2001
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              Do I understand correctlythat you object to my keeping
              my own database and making it available?


              ----- Original Message -----
              From: <jfoug@...>
              To: <primenumbers@yahoogroups.com>
              Sent: Sunday, September 30, 2001 9:30 AM
              Subject: [PrimeNumbers] Re: Prime GAP of 82794


              > Why is it "deficient" Milton? Because this example does not fit?
              > Well there is not that much special about your find. Yes, it is
              > outside of the normal bounds a little, but not too far outside those
              > bounds for numbers as large as you are working with. For a pair of
              > numbers this size, you need a gap of over 115000 to qualify for Pauls
              > list. I see nothing wrong with that, your numbers simply are not
              > special enough. You will probably have a hard time finding gaps
              > which work if ALL you do is search 10^n-k to 10^n+j. A search like
              > you are doing is no better than simply starting at 10^n+1 and
              > proceeding forward to 10^n+3, 10^n+5, ... until you find a gap of
              > sufficient size. This is a very slow method of search, and for you
              > to limit yourself to 10^n-k to 10^n+j you have doomed yourself to this
              > method. The method I described in earlier emails can speed up this
              > searc by a factor of (D-1) and with D being 10 or more, that means
              > that you can search up to 9 times faster.
              >
              > --- In primenumbers@y..., "Milton Brown" <miltbrown@e...> wrote:
              > >
              > > Your database seems to be deficient, and its
              > > not even published. I think I will make my own.
              > >
              > >
              > > ----- Original Message -----
              > > From: "Paul Leyland" <pleyland@m...>
              > > To: "Milton Brown" <miltbrown@e...>; <primenumbers@y...>
              > > Sent: Sunday, September 30, 2001 2:00 AM
              > > Subject: RE: [PrimeNumbers] Prime GAP of 82794
              > >
              > >
              > >
              > > > There are no prime numbers between
              > > >
              > > > 10^5020+47311
              > > >
              > > > and
              > > >
              > > > 10^5020-35483
              > > >
              > > > yielding a prime GAP of 82794 (or 82795).
              > >
              > > I make 82794/ln(10^5020+47311) about 7.163.
              > >
              > > Well short of the 10.0 needed to get on my top-20 page. The latter,
              > > BTW, is now under construction and I hope to make it public within
              > a day
              > > or two.
              > >
              > > Paul
              >
              >
              >
              > Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com
              > The Prime Pages : http://www.primepages.org
              >
              >
              >
              > Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
              >
              >
            • Jim Fougeron
              ... Absolutely not. An additional database would be a fine addition. I am not sure which of the lines I wrote which you read between, that stated I objected
              Message 6 of 14 , Sep 30, 2001
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                At 09:40 AM 9/30/01 -0700, Milton Brown wrote:
                >
                >Do I understand correctlythat you object to my keeping
                >my own database and making it available?

                Absolutely not. An additional database would be a fine addition. I am
                not sure which of the lines I wrote which you read between, that stated
                I objected to your keeping a database, oh well, I guess my ignorance
                shows.

                Jim.

                >----- Original Message -----
                >From: <jfoug@...>
                >To: <primenumbers@yahoogroups.com>
                >Sent: Sunday, September 30, 2001 9:30 AM
                >Subject: [PrimeNumbers] Re: Prime GAP of 82794
                >
                >
                >> Why is it "deficient" Milton? Because this example does not fit?
                >> Well there is not that much special about your find. Yes, it is
                >> outside of the normal bounds a little, but not too far outside those
                >> bounds for numbers as large as you are working with. For a pair of
                >> numbers this size, you need a gap of over 115000 to qualify for Pauls
                >> list. I see nothing wrong with that, your numbers simply are not
                >> special enough. You will probably have a hard time finding gaps
                >> which work if ALL you do is search 10^n-k to 10^n+j. A search like
                >> you are doing is no better than simply starting at 10^n+1 and
                >> proceeding forward to 10^n+3, 10^n+5, ... until you find a gap of
                >> sufficient size. This is a very slow method of search, and for you
                >> to limit yourself to 10^n-k to 10^n+j you have doomed yourself to this
                >> method. The method I described in earlier emails can speed up this
                >> searc by a factor of (D-1) and with D being 10 or more, that means
                >> that you can search up to 9 times faster.
                >>
                >> --- In primenumbers@y..., "Milton Brown" <miltbrown@e...> wrote:
                >> >
                >> > Your database seems to be deficient, and its
                >> > not even published. I think I will make my own.
                >> >
                >> >
                >> > ----- Original Message -----
                >> > From: "Paul Leyland" <pleyland@m...>
                >> > To: "Milton Brown" <miltbrown@e...>; <primenumbers@y...>
                >> > Sent: Sunday, September 30, 2001 2:00 AM
                >> > Subject: RE: [PrimeNumbers] Prime GAP of 82794
                >> >
                >> >
                >> >
                >> > > There are no prime numbers between
                >> > >
                >> > > 10^5020+47311
                >> > >
                >> > > and
                >> > >
                >> > > 10^5020-35483
                >> > >
                >> > > yielding a prime GAP of 82794 (or 82795).
                >> >
                >> > I make 82794/ln(10^5020+47311) about 7.163.
                >> >
                >> > Well short of the 10.0 needed to get on my top-20 page. The latter,
                >> > BTW, is now under construction and I hope to make it public within
                >> a day
                >> > or two.
                >> >
                >> > Paul
                >>
                >>
                >>
                >> Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com
                >> The Prime Pages : http://www.primepages.org
                >>
                >>
                >>
                >> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
                >>
                >>
                >
              • Paul Leyland
                ... Go ahead. Mine is certainly both deficient and unpublished. I aim to remedy both of those in the near future. Paul
                Message 7 of 14 , Oct 1, 2001
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                  > Your database seems to be deficient, and its
                  > not even published. I think I will make my own.

                  Go ahead.

                  Mine is certainly both deficient and unpublished. I aim to remedy both
                  of those in the near future.


                  Paul
                • Barbara and Joe
                  Paul, notwithstanding Milton s efforts, it does seem that very little effort is required to produce scores greater than 10. For example, I ran 2^201+1 to
                  Message 8 of 14 , Oct 3, 2001
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                    Paul,

                    notwithstanding Milton's efforts, it does seem that very little effort is required to produce scores greater than 10. For example, I ran 2^201+1 to 2^201+10^7-1 through Newpgen then pfgw in a couple of hours and found a gap that scores 11+. Could I suggest to potential contributors so Paul's soon to arrive webpage on the subject that :

                    1) additional criteria be added for qualification - this might become more evident when the first lists are available.
                    2) an exhaustive survey of 2^x+1 to 2^x+y-1 for x >= 100 and y = 10^7, 10^8 or even 10^9.

                    Joe.
                    > There are no prime numbers between
                    >
                    > 10^5020+47311
                    >
                    > and
                    >
                    > 10^5020-35483
                    >
                    > yielding a prime GAP of 82794 (or 82795).

                    I make 82794/ln(10^5020+47311) about 7.163.

                    Well short of the 10.0 needed to get on my top-20 page. The latter,
                    BTW, is now under construction and I hope to make it public within a day
                    or two.

                    Paul


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                    [Non-text portions of this message have been removed]
                  • Phil Carmody
                    ... *cough* *cough* - if your version of PFGW is more than 2 months old, grab the latest version of it - I don t know why, but it is amazingly 6% faster
                    Message 9 of 14 , Oct 3, 2001
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                      On Wed, 03 October 2001, "Barbara and Joe" wrote:
                      > notwithstanding Milton's efforts, it does seem that very little effort is required to produce scores greater than 10. For example, I ran 2^201+1 to 2^201+10^7-1 through Newpgen then pfgw in a couple of hours and found a gap that scores 11+. Could I suggest to potential contributors so Paul's soon to arrive webpage on the subject that :


                      *cough* *cough* - if your version of PFGW is more than 2 months old, grab the latest version of it - I don't know why, but it is amazingly 6% faster accross the board (Microstar MT7 Turbo, Duron 900)

                      > 1) additional criteria be added for qualification - this might become more evident when the first lists are available.
                      > 2) an exhaustive survey of 2^x+1 to 2^x+y-1 for x >= 100 and y = 10^7, 10^8 or even 10^9.

                      Au contraire. If there is something witty to be found there, then don't legislate it out, let it be discovered. Let it be exploited. Let those who can exploit exploit. If there are loopholes, then surely the smarts to discover them should be rewarded with fame (and fortune, and everything that goes with it).

                      As long as noone expects Paul to update the lists in real time, then the rules can be as lax as anything.

                      I wish I now had the CPU power to exploit this, and if I did, then I would wish I had the smarts too!

                      Go for it. Go for it one and all. Nothing can be gained from this apart from progress. (and I ain't 'fraid of that)

                      Phil

                      Mathematics should not have to involve martyrdom;
                      Support Eric Weisstein, see http://mathworld.wolfram.com
                      Find the best deals on the web at AltaVista Shopping!
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                    • gchil0@pop.uky.edu
                      Hi, ... I second (third, fourth?) that. Spending a couple of hours on 2^222+k using Jim s CPAPSieve and Gapper, I found the following prime gaps: 2^222+k:
                      Message 10 of 14 , Oct 3, 2001
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                        Hi,

                        > notwithstanding Milton's efforts, it does seem that very little
                        > effort is required to produce scores greater than 10. For example, I
                        > ran 2^201+1 to 2^201+10^7-1 through Newpgen then pfgw in a couple of
                        > hours and found a gap that scores 11+.

                        I second (third, fourth?) that. Spending a couple of hours on 2^222+k
                        using Jim's CPAPSieve and Gapper, I found the following prime gaps:

                        2^222+k:
                        k=385810479, 385812547, L=2068, D=13.44
                        k=377030973, 377033265, L=2292, D=14.89
                        k=2904881407, 2904883713, L=2306, D=14.99
                        k=3146587153, 3146589463, L=2310, D=15.01
                        k=4010309389, 4010311705, L=2316, D=15.05
                        k=1219497097, 1219499439, L=2342, D=15.22
                        k=2930700145, 2930702499, L=2354, D=15.30
                        k=1334629339, 1334631747, L=2408, D=15.65
                        k=3471270103, 3471272527, L=2424, D=15.75

                        > 1) additional criteria be added for qualification - this might
                        > become more evident when the first lists are available.

                        I don't think this is needed. Simply restricting the lists to 20
                        entries will quickly raise the bar needed to qualify.

                        Greg
                      • Paul Leyland
                        There still seems to be misunderstanding about what my tables are intended to contain. They are *not* a complete list of all prime gaps known with length
                        Message 11 of 14 , Oct 4, 2001
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                          There still seems to be misunderstanding about what my tables are
                          intended to contain.

                          They are *not* a complete list of all prime gaps known with length >
                          1000.
                          They are *not* a complete list of all prime gaps with length/logp > 10.0

                          They are, or rather will be, the 20 gaps of largest known length with
                          length/logp > 10.0 and the 20 gaps with length >1000 and with the
                          largest known values of length/logp.

                          Anyone who wants anything different is entirely free to do it
                          themselves.


                          Paul


                          -----Original Message-----
                          From: Barbara and Joe
                          [mailto:the_mcleans@...]
                          Sent: 03 October 2001 19:55
                          To: Prime Numbers; Paul Leyland
                          Subject: Re: [PrimeNumbers] Prime GAP of 82794


                          Paul,

                          notwithstanding Milton's efforts, it does seem that very little
                          effort is required to produce scores greater than 10. For example, I ran
                          2^201+1 to 2^201+10^7-1 through Newpgen then pfgw in a couple of hours
                          and found a gap that scores 11+. Could I suggest to potential
                          contributors so Paul's soon to arrive webpage on the subject that :

                          1) additional criteria be added for qualification - this might
                          become more evident when the first lists are available.
                          2) an exhaustive survey of 2^x+1 to 2^x+y-1 for x >= 100 and y =
                          10^7, 10^8 or even 10^9.

                          Joe.

                          > There are no prime numbers between
                          >
                          > 10^5020+47311
                          >
                          > and
                          >
                          > 10^5020-35483
                          >
                          > yielding a prime GAP of 82794 (or 82795).

                          I make 82794/ln(10^5020+47311) about 7.163.

                          Well short of the 10.0 needed to get on my top-20 page.
                          The latter,
                          BTW, is now under construction and I hope to make it
                          public within a day
                          or two.

                          Paul



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                          [Non-text portions of this message have been removed]
                        • Paul Leyland
                          ... Thanks for these. ... Halleluia! Someone, at long last, has seen the light! Thanks Greg. Paul
                          Message 12 of 14 , Oct 4, 2001
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                            > 2^222+k:
                            > k=385810479, 385812547, L=2068, D=13.44
                            > k=377030973, 377033265, L=2292, D=14.89
                            > k=2904881407, 2904883713, L=2306, D=14.99
                            > k=3146587153, 3146589463, L=2310, D=15.01
                            > k=4010309389, 4010311705, L=2316, D=15.05
                            > k=1219497097, 1219499439, L=2342, D=15.22
                            > k=2930700145, 2930702499, L=2354, D=15.30
                            > k=1334629339, 1334631747, L=2408, D=15.65
                            > k=3471270103, 3471272527, L=2424, D=15.75

                            Thanks for these.

                            >
                            > > 1) additional criteria be added for qualification - this might
                            > > become more evident when the first lists are available.
                            >
                            > I don't think this is needed. Simply restricting the lists to 20
                            > entries will quickly raise the bar needed to qualify.

                            Halleluia! Someone, at long last, has seen the light!

                            Thanks Greg.


                            Paul
                          • Hans.Rosenthal@t-online.de
                            ... Also using Jim s CPAPSieve and Gapper, I found this prime gap 1026/ln(10^20+603345152719)=D=22.279 But this D is *many miles* away from Bertil Nyman s
                            Message 13 of 14 , Oct 5, 2001
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                              gchil0@... wrote:

                              > I second (third, fourth?) that. Spending a couple of hours on 2^222+k
                              > using Jim's CPAPSieve and Gapper, I found the following prime gaps:
                              >
                              > 2^222+k:
                              > k=385810479, 385812547, L=2068, D=13.44
                              > k=377030973, 377033265, L=2292, D=14.89
                              > k=2904881407, 2904883713, L=2306, D=14.99
                              > k=3146587153, 3146589463, L=2310, D=15.01
                              > k=4010309389, 4010311705, L=2316, D=15.05
                              > k=1219497097, 1219499439, L=2342, D=15.22
                              > k=2930700145, 2930702499, L=2354, D=15.30
                              > k=1334629339, 1334631747, L=2408, D=15.65
                              > k=3471270103, 3471272527, L=2424, D=15.75
                              >
                              > > 1) additional criteria be added for qualification - this might
                              > > become more evident when the first lists are available.
                              >
                              > I don't think this is needed. Simply restricting the lists to 20
                              > entries will quickly raise the bar needed to qualify.

                              Also using Jim's CPAPSieve and Gapper, I found this prime gap

                              1026/ln(10^20+603345152719)=D=22.279

                              But this D is *many miles* away from Bertil Nyman's

                              1026/ln(14337646064565977)=D=27.579
                              or
                              1132/ln(1693182318747503)=D=32.282

                              So if you want to find a record D > 10, L > 1000
                              you should first have a close look at the end of

                              http://www.trnicely.net/gaps/gaplist.html

                              Paul L.: This would easily fill your first published
                              D > 10, L > 1000 table, if Bertil would submit his
                              findings to it ;)

                              Hans

                              PS: Though I'm sure Jim's CPAPSieve and Gapper will find
                              D's > 33 when some make heavy use of them.
                            • Barbara and Joe
                              Sorry for the delay in replying to this. It was never my understanding that the tables would be allowed to grow and grow. I just meant to imply that initially
                              Message 14 of 14 , Oct 7, 2001
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                                Sorry for the delay in replying to this. It was never my understanding that the tables would be allowed to grow and grow. I just meant to imply that initially the tables will be subject to constant heavy updating and that more resticted criteria would slow this down a bit. I hope to be able to contribute when I get myself organised.

                                Joe.

                                There still seems to be misunderstanding about what my tables are
                                intended to contain.

                                They are *not* a complete list of all prime gaps known with length >
                                1000.
                                They are *not* a complete list of all prime gaps with length/logp > 10.0

                                They are, or rather will be, the 20 gaps of largest known length with
                                length/logp > 10.0 and the 20 gaps with length >1000 and with the
                                largest known values of length/logp.

                                Anyone who wants anything different is entirely free to do it
                                themselves.


                                Paul


                                -----Original Message-----
                                From: Barbara and Joe
                                [mailto:the_mcleans@...]
                                Sent: 03 October 2001 19:55
                                To: Prime Numbers; Paul Leyland
                                Subject: Re: [PrimeNumbers] Prime GAP of 82794


                                Paul,

                                notwithstanding Milton's efforts, it does seem that very little
                                effort is required to produce scores greater than 10. For example, I ran
                                2^201+1 to 2^201+10^7-1 through Newpgen then pfgw in a couple of hours
                                and found a gap that scores 11+. Could I suggest to potential
                                contributors so Paul's soon to arrive webpage on the subject that :

                                1) additional criteria be added for qualification - this might
                                become more evident when the first lists are available.
                                2) an exhaustive survey of 2^x+1 to 2^x+y-1 for x >= 100 and y =
                                10^7, 10^8 or even 10^9.

                                Joe.

                                > There are no prime numbers between
                                >
                                > 10^5020+47311
                                >
                                > and
                                >
                                > 10^5020-35483
                                >
                                > yielding a prime GAP of 82794 (or 82795).

                                I make 82794/ln(10^5020+47311) about 7.163.

                                Well short of the 10.0 needed to get on my top-20 page.
                                The latter,
                                BTW, is now under construction and I hope to make it
                                public within a day
                                or two.

                                Paul



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                                083388:HM/A=799560/R=2/*http://shop.store.yahoo.com/cgi-bin/clink?overst
                                ock3+shopping:dmad/M=168643.1620686.3168692.1261774/D=egroupweb/S=170508
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                                verstock.com/rmi-framed-url/http://www.overstock.com/cgi-bin/d2.cgi%3Fci
                                d=12715>

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                                pmail/S=1705083388:HM/A=799560/rand=686505806>

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