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RE: [PrimeNumbers] New prime gap L=2000

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  • Phil Carmody
    ... Something as simple as
    Message 1 of 21 , Nov 2, 2001
      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+$a a: from 0 to 2028 and I got that : 2^116+5766300710013+0 is composite: (0.000000 seconds) and primeform.exe gave :
      Message 2 of 21 , Nov 2, 2001
        I tried this :
        ABC2 2^116+5766300710013+$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 3 of 21 , Nov 2, 2001
          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 4 of 21 , Nov 2, 2001
            --- 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 5 of 21 , Nov 2, 2001
              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 6 of 21 , Nov 2, 2001
                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 7 of 21 , Nov 6, 2001
                  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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                  >
                  >
                  >
                  > Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service.
                  >
                  >
                  >
                  > [Non-text portions of this message have been removed]
                  >
                  >
                  > 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/
                  >
                  >
                • 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 8 of 21 , Nov 7, 2001
                    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 9 of 21 , Nov 14, 2001
                      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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