Re: New prime gap L=2000

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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
Message 1 of 21 , Nov 2, 2001
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This is a round off problem exhibited in release build 1.1

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
> 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
• I m trying to make use too! Is there any organised search? Joe. ... From: Hans.Rosenthal@t-online.de To:
Message 2 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@...>
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

Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com
The Prime Pages : http://www.primepages.org

[Non-text portions of this message have been removed]
• 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 3 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@...>
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@...>
> 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
>
>
>
>
>
> Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com
> The Prime Pages : http://www.primepages.org
>
>
>
>
>
>
> [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/
>
>
• ... 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 4 of 21 , Nov 7, 2001
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> 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
• 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 5 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@...>
Date: 07 November 2001 18:09
Subject: Re: [PrimeNumbers] New prime gap L=2000

>
>> 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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