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RE: [PrimeNumbers] Prime GAP of 82794

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  • Paul Leyland
    ... Go ahead. Mine is certainly both deficient and unpublished. I aim to remedy both of those in the near future. Paul
    Message 1 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      Mine is certainly both deficient and unpublished.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 2 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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      • 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 3 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;
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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 4 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 5 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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            • Paul Leyland
              ... Thanks for these. ... Halleluia! Someone, at long last, has seen the light! Thanks Greg. Paul
              Message 6 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 7 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 8 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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                    ock3+shopping:dmad/M=168643.1620686.3168692.1261774/D=egroupweb/S=170508
                    3388:HM/A=799560/R=3/1001840419+http://us.rmi.yahoo.com/rmi/http://www.o
                    verstock.com/rmi-framed-url/http://www.overstock.com/cgi-bin/d2.cgi%3Fci
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