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Prime gaps pages

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  • Paul Leyland
    Sorry, I forgot to set the Subject: line correctly. Please use this one for any replies, or things will get hopelessly confusing. Paul ...
    Message 1 of 21 , Oct 9, 2001
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      Sorry, I forgot to set the Subject: line correctly. Please use this
      one for any replies, or things will get hopelessly confusing.


      Paul

      > -----Original Message-----
      > From: Paul Leyland [mailto:pleyland@...]
      > Sent: 09 October 2001 17:26
      > To: primenumbers@yahoogroups.com
      > Subject: RE: [PrimeNumbers] SPSP lists
      >
      >
      > After a longer delay than I would have liked, the first cut at a table
      > of prime gaps which are both long --- L = p2-p1 > 1000 ---
      > and unusually
      > large --- D = (p2-p1)/ln(p2) --- is available for limited viewing.
      >
      > The URL is
      > http://research.microsoft.com/~pleyland/primes/gaps20.htm and
      > there are no known links to it from elsewhere --- hence the "limited
      > viewing" comment above.
      >
      > I'm fairly sure that the table sorted by D won't need too
      > much revision
      > in the near future. I'm absolutely certain that the one sorted by L
      > will need revision, not least because it only has six entries in it so
      > far and more could be added from the other table. However,
      > members of
      > primes-list should be able to find another 14 gaps with L >
      > 2000 and D >
      > 10.0 in short order, so the spaces are left for you to fill.
      >
      > Please send me entries for either list, but first ensure they meet the
      > entry requirements. If D < 10.0 or L < 1000, I'm not
      > interested. To get
      > in the high-D list you need a score of at least 27.7
      >
      > Also, please send me any corrections for errors that may have
      > crept in.
      > Please note that the "Date" column records when I became aware of the
      > entry, not when the gap may have been found. This criterion
      > may change.
      >
      > Once the high-L list has filled, the page will be linked to from
      > elsewhere and so should start appearing in search engines, etc.
      >
      >
      > Thanks,
      > Paul
      >
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      >
      >
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    • Hadley, Thomas H (Tom), NLCIO
      Thanks, Paul. This looks like a very interesting page and the link to Nicely s page is great. I almost posted this morning to ask you what the status of this
      Message 2 of 21 , Oct 9, 2001
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        Thanks, Paul. This looks like a very interesting page and the link to
        Nicely's page is great.

        I almost posted this morning to ask you what the status of this page was,
        but that was apparently unnecessary!

        Tom Hadley

        -----Original Message-----
        From: Paul Leyland [mailto:pleyland@...]
        Sent: Tuesday, October 09, 2001 11:42 AM
        To: primenumbers@yahoogroups.com
        Subject: [PrimeNumbers] Prime gaps pages


        Sorry, I forgot to set the Subject: line correctly. Please use this
        one for any replies, or things will get hopelessly confusing.


        Paul

        > -----Original Message-----
        > From: Paul Leyland [mailto:pleyland@...]
        > Sent: 09 October 2001 17:26
        > To: primenumbers@yahoogroups.com
        > Subject: RE: [PrimeNumbers] SPSP lists
        >
        >
        > After a longer delay than I would have liked, the first cut at a table
        > of prime gaps which are both long --- L = p2-p1 > 1000 ---
        > and unusually
        > large --- D = (p2-p1)/ln(p2) --- is available for limited viewing.
        >
        > The URL is
        > http://research.microsoft.com/~pleyland/primes/gaps20.htm and
        > there are no known links to it from elsewhere --- hence the "limited
        > viewing" comment above.
        >
        > I'm fairly sure that the table sorted by D won't need too
        > much revision
        > in the near future. I'm absolutely certain that the one sorted by L
        > will need revision, not least because it only has six entries in it so
        > far and more could be added from the other table. However,
        > members of
        > primes-list should be able to find another 14 gaps with L >
        > 2000 and D >
        > 10.0 in short order, so the spaces are left for you to fill.
        >
        > Please send me entries for either list, but first ensure they meet the
        > entry requirements. If D < 10.0 or L < 1000, I'm not
        > interested. To get
        > in the high-D list you need a score of at least 27.7
        >
        > Also, please send me any corrections for errors that may have
        > crept in.
        > Please note that the "Date" column records when I became aware of the
        > entry, not when the gap may have been found. This criterion
        > may change.
        >
        > Once the high-L list has filled, the page will be linked to from
        > elsewhere and so should start appearing in search engines, etc.
        >
        >
        > Thanks,
        > Paul
        >
        > ------------------------ Yahoo! Groups Sponsor
        > ---------------------~-->
        > FREE COLLEGE MONEY
        > CLICK HERE to search
        > 600,000 scholarships!
        > http://us.click.yahoo.com/Pv4pGD/4m7CAA/ySSFAA/8HYolB/TM
        > --------------------------------------------------------------
        > -------~->
        >
        > Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com
        > The Prime Pages : http://www.primepages.org
        >
        >
        >
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        http://docs.yahoo.com/info/terms/




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      • Nuutti Kuosa
        Hello, I have used little time to search primegaps larger than 10 000 numbers. Here are my findings : 2^999 : Found gap of 10248 at 2^999+250941671 to
        Message 3 of 21 , Oct 9, 2001
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          Hello,

          I have used little time to search primegaps larger than 10 000 numbers.

          Here are my findings :


          2^999 : Found gap of 10248 at 2^999+250941671 to 2^999+250951919
          digits : 301 and D = 14,80



          2^799 : Found gap of 10686 at 2^799+18220344359 to 2^799+18220355045
          digits : 241 and D = 19,29

          ( I am not 100 % sure that I have calculated these D values correctly, Paul
          please check
          that)

          Both gaps have been found using CPAPSieve and Gapper made by Jim Fougeron.
          Then gaps have been checked using pfge.exe and
          endpoints verified being primes using primo 1.0.


          Yours,

          Nuutti
        • jfoug@kdsi.net
          ... numbers. ... Nuutti, You have calculated D correctly. Let me state that this is a pretty darn good find. L=10000 and D~=20 is a substantial gap on a
          Message 4 of 21 , Oct 9, 2001
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            --- In primenumbers@y..., "Nuutti Kuosa" <nuutti.kuosa@i...> wrote:
            >
            > Hello,
            >
            > I have used little time to search primegaps larger than 10 000
            numbers.
            >
            > Here are my findings :
            >
            >
            > 2^999 : Found gap of 10248 at 2^999+250941671 to 2^999+250951919
            > digits : 301 and D = 14,80
            >
            >
            >
            > 2^799 : Found gap of 10686 at 2^799+18220344359 to 2^799+18220355045
            > digits : 241 and D = 19,29

            Nuutti,

            You have calculated D correctly. Let me state that this is a pretty
            darn good find. L=10000 and D~=20 is a substantial gap on a
            not-trivial number.

            Jim.

            > ( I am not 100 % sure that I have calculated these D values
            correctly, Paul
            > please check
            > that)
            >
            > Both gaps have been found using CPAPSieve and Gapper made by Jim
            Fougeron.
            > Then gaps have been checked using pfge.exe and
            > endpoints verified being primes using primo 1.0.
            >
            >
            > Yours,
            >
            > Nuutti
          • Phil Carmody
            ... Indeed. I was looking at the two tables the other day and had thie horrible image of a hypothetical L=5000 D=27.6 (you work out the magnitude :-0 ) just
            Message 5 of 21 , Oct 10, 2001
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              On Tue, 09 October 2001, jfoug@... wrote:
              > > 2^799 : Found gap of 10686 at 2^799+18220344359 to 2^799+18220355045
              > > digits : 241 and D = 19,29
              >
              > Nuutti,
              >
              > You have calculated D correctly. Let me state that this is a pretty
              > darn good find. L=10000 and D~=20 is a substantial gap on a
              > not-trivial number.

              Indeed. I was looking at the two tables the other day and had thie horrible image of a hypothetical L=5000 D=27.6 (you work out the magnitude :-0 ) just dropping off the bottom, due to the fact taht it will bever reach the D table, and L=5000 will soon look tiny.
              However, in my book, that hypothetical situation is more impressive than anything we currently have.

              I.e. yes, I'm opening up an old thread, I think that just those two tables on their own don't suffice.

              Either - and I don't like this suggestion that much - the addition of a "big boy's" league where the L critereon is 5000, (thus excluding Nyman's and leaving the D=20+ an open playing field again). However this is includes the introduction of more arbitrary constants, and makes the L=4996 D=27.6 look a bit stupid. That's why I don't like this suggestion, I'll be frank about that. So that's why I prefer option 2...

              Or secondly a table which is a compromise between the 'highest D s.t. L is satisfied' and 'highest L s.t. D is satisfied'. One that combines the two attributes and doesn't bias for against either.

              The latter requires pulling a weighting function out of the air.
              Would D*log(L) work?

              Nyman 32.28254764*l(1132) 227.00252217817425499557
              Nyman 27.70377788*l(1022) 191.97379343297103047509
              Dubner 18.70714821*l(7224) 166.21608159714677126104
              Dubner 22.14977782*l(2024) 168.62251590472460310671
              Kuosa 19.29 *l(10686) 178.94734532606675422055

              Let's make my hypothetical loser more realistic - D=23
              Hypothetical 23 *l(4996) 195.87703603864577077120
              i.e Bertil would find it slightly harder to dominate the entire table.
              Other functions may be more justifiable of course.

              Note - we, as a group, (now) have the database feature which can be used to store all gaps that satisfy the Leyland criteria. If they are _all_ recorded, then retrospectively new measures may be
              applied to give different views of the data.
              i.e. It doesn't require Paul to take on new work, though to be frank I think that there's a certain coherence to having all of the views on the data on the same web page.

              Phil

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            • Paul Leyland
              ... Agreed. I was impressed to receive these two entries so quickly. They are being added to the page right now and should be visible shortly. ... As I ve
              Message 6 of 21 , Oct 10, 2001
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                > > You have calculated D correctly. Let me state that this is a pretty
                > > darn good find. L=10000 and D~=20 is a substantial gap on a
                > > not-trivial number.
                >
                > Indeed. I was looking at the two tables the other day and had

                Agreed. I was impressed to receive these two entries so quickly. They
                are being added to the page right now and should be visible shortly.

                > I.e. yes, I'm opening up an old thread, I think that just
                > those two tables on their own don't suffice.

                As I've said before, anyone is free to do anything they wish with regard
                to prime gap pages --- as long as I don't have to do it for them. I
                haven't yet been convinced to put more work into this myself.

                My tables were only set up because I took seriously what seemed to have
                been intended as a throw-away remark --- that setting up such tables
                would be a never-ending and futile task.

                Anyway, we have our own resident gap-finder extraordinaire on this very
                list. Milton: perhaps you should submit some of your large gaps which
                meet the entry requirements.


                Paul
              • d.broadhurst@open.ac.uk
                Paul: Kenneth Conrow (kconrow at the obvious edu site) has posted the file npgfile.SAV at ftp://unix.ksu.edu/pub/pentadecet/ This almost certainly has suitable
                Message 7 of 21 , Oct 10, 2001
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                  Paul: Kenneth Conrow (kconrow at the obvious edu site)
                  has posted the file npgfile.SAV at
                  ftp://unix.ksu.edu/pub/pentadecet/
                  This almost certainly has suitable entries, but
                  to me it is truncated.
                  Perhaps I'm not sufficiently into MuddleSoft file types:-)
                  David
                • Nuutti Kuosa
                  Hello again, I have still used some time to search primegaps larger than 10 000 numbers. Here is my recent finding : Found gap of 10634 at 2^699+207290233605
                  Message 8 of 21 , Oct 24, 2001
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                    Hello again,

                    I have still used some time to search primegaps larger than 10 000 numbers.

                    Here is my recent finding :


                    Found gap of 10634 at 2^699+207290233605 to 2^699+207290244239
                    digits : 211 and D = 21,95

                    It was a little bit harder to find this gap than I expected.
                    k is little over 207,000,000,000

                    Both gaps have been found using CPAPSieve and Gapper made by Jim Fougeron.
                    Then gaps have been checked using pfge.exe and
                    endpoints verified being primes using primo 1.0.


                    Yours,

                    Nuutti
                  • Nuutti Kuosa
                    I have changed my target in the search of prime gaps. Now I am looking for gaps greater than 2000 digits. I started yesterday and found almost immediately
                    Message 9 of 21 , Oct 27, 2001
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                      I have changed my target in the search of prime gaps. Now I am looking for
                      gaps greater than 2000 digits.
                      I started yesterday and found almost immediately quite a good one.

                      Here :

                      Found gap of 2062 at 2^121+270755381915 to 2^121+270755383977
                      digits : 37 and D = 24.59

                      This is better than Jim Fougeron's old record :

                      2^127+64770271805 to 2^127+64770273813
                      digits : 39 and D=22.81

                      I checked all k's in the range from 1 to 1,190 billion

                      The gap has been found using CPAPSieve and Gapper made by Jim Fougeron.
                      Then the gap has been checked using pfge.exe and
                      endpoints verified to be primes using primo 1.0.


                      Yours,

                      Nuutti







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                    • Hans.Rosenthal@t-online.de
                      ... Great find, Nuutti! Now I wonder: are Nuutti and I the only prime gap hunters who make heavy use of Jim s brilliant tools? Hans
                      Message 10 of 21 , Oct 27, 2001
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                        Nuutti Kuosa wrote:
                        >
                        > I have changed my target in the search of prime gaps. Now I am looking for
                        > gaps greater than 2000 digits.
                        > I started yesterday and found almost immediately quite a good one.
                        >
                        > Here :
                        >
                        > Found gap of 2062 at 2^121+270755381915 to 2^121+270755383977
                        > digits : 37 and D = 24.59
                        >
                        > This is better than Jim Fougeron's old record :
                        >
                        > 2^127+64770271805 to 2^127+64770273813
                        > digits : 39 and D=22.81
                        >
                        > I checked all k's in the range from 1 to 1,190 billion
                        >
                        > The gap has been found using CPAPSieve and Gapper made by Jim Fougeron.
                        > Then the gap has been checked using pfge.exe and
                        > endpoints verified to be primes using primo 1.0.
                        >
                        > Yours,
                        >
                        > Nuutti

                        Great find, Nuutti!

                        Now I wonder: are Nuutti and I the only prime gap hunters who
                        make heavy use of Jim's brilliant tools?

                        Hans
                      • Paul Leyland
                        ... This is indeed a good gap. Unfortunately it doesn t make either of my two top-20 tables, which presently require D 27.70377788 or L 5538. Keep on trying,
                        Message 11 of 21 , Oct 29, 2001
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                          > Found gap of 2062 at 2^121+270755381915 to 2^121+270755383977
                          > digits : 37 and D = 24.59
                          >
                          > This is better than Jim Fougeron's old record :
                          >
                          > 2^127+64770271805 to 2^127+64770273813
                          > digits : 39 and D=22.81
                          >
                          > I checked all k's in the range from 1 to 1,190 billion
                          >
                          > The gap has been found using CPAPSieve and Gapper made by
                          > Jim Fougeron.
                          > Then the gap has been checked using pfge.exe and
                          > endpoints verified to be primes using primo 1.0.


                          This is indeed a good gap. Unfortunately it doesn't make either of my
                          two top-20 tables, which presently require D>27.70377788 or L>5538.
                          Keep on trying, and you should get one in those ranges.


                          Paul
                        • Nuutti Kuosa
                          Here is the newest one : Found gap of 2028 at 2^116+5,766,300,710,013 to 2^116+5766300712041 digits : 35 and D = 25.22 I am going to check all k s in the range
                          Message 12 of 21 , Nov 2, 2001
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                            Here is the newest one :

                            Found gap of 2028 at 2^116+5,766,300,710,013 to 2^116+5766300712041
                            digits : 35 and D = 25.22

                            I am going to check all k's in the range from 1 to 10,000 billion

                            The gap has been found using CPAPSieve and Gapper made by Jim Fougeron.
                            Then the gap has been checked using PrimeForm.exe and
                            endpoints verified to be primes using primo 1.0.

                            I had some problems with pfgw.exe when I tried to verify the gap.
                            May be the ABC2 file format does not support that big numbers.


                            Yours,

                            Nuutti
                          • Phil Carmody
                            ... Something as simple as
                            Message 13 of 21 , Nov 2, 2001
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                              On Fri, 02 November 2001, "Nuutti Kuosa" wrote:
                              > I had some problems with pfgw.exe when I tried to verify the gap.
                              > May be the ABC2 file format does not support that big numbers.

                              Something as simple as
                              <<<
                              ABC2 _your_initial_prime_here_ + $a
                              a: from 0 to _your_gap_length_here_
                              >>>

                              should work. 'step 2' can be added to skip the evens!

                              Phil

                              Mathematics should not have to involve martyrdom;
                              Support Eric Weisstein, see http://mathworld.wolfram.com
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                            • Nuutti Kuosa
                              I tried this : ABC2 2^116+5766300710013+$a a: from 0 to 2028 and I got that : 2^116+5766300710013+0 is composite: (0.000000 seconds) and primeform.exe gave :
                              Message 14 of 21 , Nov 2, 2001
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                                I tried this :
                                ABC2 2^116+5766300710013+$a
                                a: from 0 to 2028

                                and I got that :
                                2^116+5766300710013+0 is composite: (0.000000 seconds)

                                and primeform.exe gave :
                                2^116+5766300710013+0 is probable prime! (a = 4243) (digits:35)

                                Yours,

                                Nuutti

                                -----Original Message-----
                                From: Phil Carmody [mailto:fatphil@...]
                                Sent: 2. marraskuuta 2001 18:40
                                To: primenumbers@yahoogroups.com
                                Subject: RE: [PrimeNumbers] New prime gap L=2000


                                On Fri, 02 November 2001, "Nuutti Kuosa" wrote:
                                > I had some problems with pfgw.exe when I tried to verify the gap.
                                > May be the ABC2 file format does not support that big numbers.

                                Something as simple as
                                <<<
                                ABC2 _your_initial_prime_here_ + $a
                                a: from 0 to _your_gap_length_here_
                                >>>

                                should work. 'step 2' can be added to skip the evens!

                                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!
                                http://www.shopping.altavista.com


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                              • Hadley, Thomas H (Tom), NLCIO
                                ... Interesting. I wanted to see which program was right so I used factor.exe (I forget where on the web this came from.) I found what appears to be a bug
                                Message 15 of 21 , Nov 2, 2001
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                                  Nuutti wrote:
                                  >I tried this :
                                  >ABC2 2^116+5766300710013+$a
                                  >a: from 0 to 2028
                                  >
                                  >and I got that :
                                  >2^116+5766300710013+0 is composite: (0.000000 seconds)
                                  >
                                  >and primeform.exe gave :
                                  >2^116+5766300710013+0 is probable prime! (a = 4243) (digits:35)
                                  >
                                  Interesting. I wanted to see which program was right so I used "factor.exe"
                                  (I forget where on the web this came from.) I found what appears to be a
                                  bug in factor.exe.

                                  When I ran "factor -f 2#116+5766300710013" I got:
                                  83076749736557242056487939427153021
                                  ...
                                  PRIME FACTOR 20331551783
                                  COMPOSITE FACTOR 4086099803066726009011387

                                  However, the number it factored, (...3021) is NOT 2^116+5766300710013.
                                  In fact it differs from this number by 2^32*17*79. This is an indication to
                                  me that factor.exe has a bug in calculating the value on the command line or
                                  that it is not designed to handle the addition of a number more than 32
                                  bits.

                                  Perhaps pfgw has this same problem??

                                  When I ran "factor 83076749736557242056493707568231549", which is the
                                  correct value for 2^116+5766300710013, I got:
                                  this number is prime!

                                  Hoping I made no typos,

                                  Tom
                                • jfoug@kdsi.net
                                  ... used factor.exe ... to be a ... The factor.exe file certainly has bugs. it uses integer (or float) numbers when building expressions, instead of Miracl
                                  Message 16 of 21 , Nov 2, 2001
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                                    --- In primenumbers@y..., "Hadley, Thomas H (Tom), NLCIO"
                                    <thadley@a...> wrote:
                                    > Nuutti wrote:
                                    > >I tried this :
                                    > >ABC2 2^116+5766300710013+$a
                                    > >a: from 0 to 2028
                                    > >
                                    > >and I got that :
                                    > >2^116+5766300710013+0 is composite: (0.000000 seconds)
                                    > >
                                    > >and primeform.exe gave :
                                    > >2^116+5766300710013+0 is probable prime! (a = 4243) (digits:35)
                                    > >
                                    > Interesting. I wanted to see which program was right so I
                                    used "factor.exe"
                                    > (I forget where on the web this came from.) I found what appears
                                    to be a
                                    > bug in factor.exe.

                                    The factor.exe file certainly has bugs. it uses integer (or float)
                                    numbers when building expressions, instead of Miracl numbers.

                                    > When I ran "factor -f 2#116+5766300710013" I got:
                                    > 83076749736557242056487939427153021
                                    > ...
                                    > PRIME FACTOR 20331551783
                                    > COMPOSITE FACTOR 4086099803066726009011387
                                    >
                                    > However, the number it factored, (...3021) is NOT
                                    2^116+5766300710013.
                                    > In fact it differs from this number by 2^32*17*79. This is an
                                    indication to
                                    > me that factor.exe has a bug in calculating the value on the
                                    command line or
                                    > that it is not designed to handle the addition of a number more
                                    than 32
                                    > bits.
                                    >
                                    > Perhaps pfgw has this same problem??
                                    >
                                    > When I ran "factor 83076749736557242056493707568231549", which is
                                    the
                                    > correct value for 2^116+5766300710013, I got:
                                    > this number is prime!
                                    >
                                    > Hoping I made no typos,
                                    >
                                    > Tom
                                  • jfoug@kdsi.net
                                    Short answer: This is a round off problem exhibited in release build 1.1 Long answer: In the 1.1 release of PFGW, when it builds the FFT s, it finds which FFT
                                    Message 17 of 21 , Nov 2, 2001
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                                      Short answer:
                                      This is a round off problem exhibited in release build 1.1

                                      Long answer:
                                      In the 1.1 release of PFGW, when it builds the FFT's, it finds which
                                      FFT size to use, and simply used it with the number of bits per limb
                                      listed. The FFT size selected for this number was 32,23 (32 fft
                                      limbs at 23 bits per limb). However, this number only requires
                                      5.04 limbs (at 32 bits per limb), so it was simply "shoved" down
                                      into the bottom of the FFT number. There is a current development
                                      version of PFGW which behaves differently when building the FFT
                                      contexts. It knows that this number fits into a 32,23 FFT, but it
                                      then looks and finds that it fits in a 32,22 or a 32,21 ... or a
                                      32,16. It choses to use a 32,16 (32 limbs with 16 bits per limb).
                                      This eliminates ANY possiblity of round off issues, while still
                                      processing the number using 32 FFT elements (same speed).

                                      Within the current release 1.1 PFGW, there is a option which forces
                                      pfgw to select a FFT using fewer than maximal number of bits. This
                                      is the authentication function. Simply putting -a1 on the command
                                      line switch will force PFGW to use 1 less bit per limb (possibly
                                      causing it to have to use more limbs also). This helps reduce the
                                      issues of FFT round off by using FFT's with less bits of precision
                                      per limb. There is also a -a2 which reduces the number of bits
                                      per limb by 2 bits. The drawback to 1 or 2 bits less per limb is
                                      felt when this causes the number of FFT limbs to increase. When the
                                      number of limbs increases, this causes a 20-65% slowdown for testing
                                      the number.

                                      One huge point of clarification. Using a tool such as PFGW which
                                      uses FFT numbers exclusivly is a huge overkill. It is like duck
                                      hunting with a tank. Sure it works, but it is probably far from
                                      optimal. PFGW is probably at least 10 to 50 times slower on numbers
                                      of this size than a program which uses "classical" or Karatsuba math,
                                      such as GMP or Miracl. I am not sure if there currently is a GMP
                                      program which does things like PFGW does, but for numbers under
                                      2^1000, a program like that would be preferable over the current
                                      FFT only PFGW.

                                      Jim.

                                      --- In primenumbers@y..., "Nuutti Kuosa" <nuutti.kuosa@i...> wrote:
                                      > I tried this :
                                      > ABC2 2^116+5766300710013+$a
                                      > a: from 0 to 2028
                                      >
                                      > and I got that :
                                      > 2^116+5766300710013+0 is composite: (0.000000 seconds)
                                      >
                                      > and primeform.exe gave :
                                      > 2^116+5766300710013+0 is probable prime! (a = 4243) (digits:35)
                                      >
                                      > Yours,
                                      >
                                      > Nuutti
                                      >
                                      > -----Original Message-----
                                      > From: Phil Carmody [mailto:fatphil@a...]
                                      > Sent: 2. marraskuuta 2001 18:40
                                      > To: primenumbers@y...
                                      > Subject: RE: [PrimeNumbers] New prime gap L=2000
                                      >
                                      >
                                      > On Fri, 02 November 2001, "Nuutti Kuosa" wrote:
                                      > > I had some problems with pfgw.exe when I tried to verify the gap.
                                      > > May be the ABC2 file format does not support that big numbers.
                                      >
                                      > Something as simple as
                                      > <<<
                                      > ABC2 _your_initial_prime_here_ + $a
                                      > a: from 0 to _your_gap_length_here_
                                      > >>>
                                      >
                                      > should work. 'step 2' can be added to skip the evens!
                                      >
                                      > Phil
                                    • Barbara and Joe
                                      I m trying to make use too! Is there any organised search? Joe. ... From: Hans.Rosenthal@t-online.de To:
                                      Message 18 of 21 , Nov 2, 2001
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                                        I'm trying to make use too!

                                        Is there any organised search?

                                        Joe.
                                        -----Original Message-----
                                        From: Hans.Rosenthal@... <Hans.Rosenthal@...>
                                        To: primenumbers@yahoogroups.com <primenumbers@yahoogroups.com>
                                        Date: 28 October 2001 02:55
                                        Subject: Re: [PrimeNumbers] New prime gap L=2000


                                        Nuutti Kuosa wrote:
                                        >
                                        > I have changed my target in the search of prime gaps. Now I am looking for
                                        > gaps greater than 2000 digits.
                                        > I started yesterday and found almost immediately quite a good one.
                                        >
                                        > Here :
                                        >
                                        > Found gap of 2062 at 2^121+270755381915 to 2^121+270755383977
                                        > digits : 37 and D = 24.59
                                        >
                                        > This is better than Jim Fougeron's old record :
                                        >
                                        > 2^127+64770271805 to 2^127+64770273813
                                        > digits : 39 and D=22.81
                                        >
                                        > I checked all k's in the range from 1 to 1,190 billion
                                        >
                                        > The gap has been found using CPAPSieve and Gapper made by Jim Fougeron.
                                        > Then the gap has been checked using pfge.exe and
                                        > endpoints verified to be primes using primo 1.0.
                                        >
                                        > Yours,
                                        >
                                        > Nuutti

                                        Great find, Nuutti!

                                        Now I wonder: are Nuutti and I the only prime gap hunters who
                                        make heavy use of Jim's brilliant tools?

                                        Hans

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                                        [Non-text portions of this message have been removed]
                                      • Milton Brown
                                        It seems that the only organized search is by special interests that justify them by their own arbitrary interest factor ... From: Barbara and Joe
                                        Message 19 of 21 , Nov 6, 2001
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                                          It seems that the only organized search is
                                          by special interests that justify them by
                                          their own arbitrary "interest factor"


                                          ----- Original Message -----
                                          From: "Barbara and Joe" <the_mcleans@...>
                                          To: <primenumbers@yahoogroups.com>; <Hans.Rosenthal@...>
                                          Sent: Friday, November 02, 2001 3:32 PM
                                          Subject: Re: [PrimeNumbers] New prime gap L=2000


                                          > I'm trying to make use too!
                                          >
                                          > Is there any organised search?
                                          >
                                          > Joe.
                                          > -----Original Message-----
                                          > From: Hans.Rosenthal@... <Hans.Rosenthal@...>
                                          > To: primenumbers@yahoogroups.com <primenumbers@yahoogroups.com>
                                          > Date: 28 October 2001 02:55
                                          > Subject: Re: [PrimeNumbers] New prime gap L=2000
                                          >
                                          >
                                          > Nuutti Kuosa wrote:
                                          > >
                                          > > I have changed my target in the search of prime gaps. Now I am looking
                                          for
                                          > > gaps greater than 2000 digits.
                                          > > I started yesterday and found almost immediately quite a good one.
                                          > >
                                          > > Here :
                                          > >
                                          > > Found gap of 2062 at 2^121+270755381915 to 2^121+270755383977
                                          > > digits : 37 and D = 24.59
                                          > >
                                          > > This is better than Jim Fougeron's old record :
                                          > >
                                          > > 2^127+64770271805 to 2^127+64770273813
                                          > > digits : 39 and D=22.81
                                          > >
                                          > > I checked all k's in the range from 1 to 1,190 billion
                                          > >
                                          > > The gap has been found using CPAPSieve and Gapper made by Jim
                                          Fougeron.
                                          > > Then the gap has been checked using pfge.exe and
                                          > > endpoints verified to be primes using primo 1.0.
                                          > >
                                          > > Yours,
                                          > >
                                          > > Nuutti
                                          >
                                          > Great find, Nuutti!
                                          >
                                          > Now I wonder: are Nuutti and I the only prime gap hunters who
                                          > make heavy use of Jim's brilliant tools?
                                          >
                                          > Hans
                                          >
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                                          >
                                          >
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                                          >
                                          >
                                          >
                                          > [Non-text portions of this message have been removed]
                                          >
                                          >
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                                          >
                                        • Hans.Rosenthal@t-online.de
                                          ... There is indeed an organized search for (first occurrence) prime gaps. Thomas R. Nicely maintains this website http://www.trnicely.net/gaps/gaplist.html
                                          Message 20 of 21 , Nov 7, 2001
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                                            Joe McLean asked:

                                            > I'm trying to make use too!
                                            >
                                            > Is there any organised search?
                                            >
                                            > Joe.

                                            There is indeed an organized search for (first occurrence) prime
                                            gaps. Thomas R. Nicely maintains this website

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

                                            All the entries in Paul Leyland's 'largest D's' table were taken
                                            from this site.

                                            Hans
                                          • Barbara and Joe
                                            Thanks Hans, I actually meant entries for the second of Paul s tables rather than the first. I am very slowly working through some simple ranges, which hasn t
                                            Message 21 of 21 , Nov 14, 2001
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                                              Thanks Hans,

                                              I actually meant entries for the second of Paul's tables rather than the
                                              first. I am very slowly working through some simple ranges, which hasn't
                                              produced anything special yet, but may suggest certain good places to look.

                                              Joe.
                                              -----Original Message-----
                                              From: Hans Rosenthal <Hans.Rosenthal@...>
                                              To: Barbara and Joe <the_mcleans@...>
                                              Cc: primenumbers@yahoogroups.com <primenumbers@yahoogroups.com>
                                              Date: 07 November 2001 18:09
                                              Subject: Re: [PrimeNumbers] New prime gap L=2000


                                              >Joe McLean asked:
                                              >
                                              >> I'm trying to make use too!
                                              >>
                                              >> Is there any organised search?
                                              >>
                                              >> Joe.
                                              >
                                              >There is indeed an organized search for (first occurrence) prime
                                              >gaps. Thomas R. Nicely maintains this website
                                              >
                                              >http://www.trnicely.net/gaps/gaplist.html
                                              >
                                              >All the entries in Paul Leyland's 'largest D's' table were taken
                                              >from this site.
                                              >
                                              >Hans
                                              >
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