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RE: [PrimeNumbers] New prime gap L=2000

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  • Nuutti Kuosa
    I tried this : ABC2 2^116+5766300710013+$a a: from 0 to 2028 and I got that : 2^116+5766300710013+0 is composite: (0.000000 seconds) and primeform.exe gave :
    Message 1 of 21 , Nov 2, 2001
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      I tried this :
      ABC2 2^116+5766300710013+$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

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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 2 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 3 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 4 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 5 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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            • 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 6 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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                >
                >
                >
                > [Non-text portions of this message have been removed]
                >
                >
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                >
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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 7 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 8 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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