Mersenne Digest Tuesday, May 15 2001 Volume 01 : Number 852
----------------------------------------------------------------------
Date: Mon, 14 May 2001 23:33:48 +0200
From: "Steinar H. Gunderson" <[EMAIL PROTECTED]>
Subject: Re: Overriding assigned exponent type (was Re: Mersenne: Re: 26 exponents)
On Mon, May 14, 2001 at 02:00:02PM -0700, Aaron Blosser wrote:
>I fear that many folks may not be aware of the list, or find
>that subscribing seems too hard (odd as that may sound to us experts :)
Or perhaps being set back by the description of an "in-depth discussion
about Mersenne primes"... ;-) When people start throwing the maths
around, I feel like I should take more maths soon :-P
Anyhow, no critique, but perhaps this _isn't_ a mailing list for the
general user. I personally like it, but the average SETI@Home `convert'
might not. Perhaps we could have a general `users' list instead?
/* Steinar */
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Date: Tue, 15 May 2001 10:43:00 -0400
From: Nathan Russell <[EMAIL PROTECTED]>
Subject: Re: Overriding assigned exponent type (was Re: Mersenne: Re: 26 exponents)
On Mon, 14 May 2001 23:33:48 +0200, Steinar H. Gunderson wrote:
>On Mon, May 14, 2001 at 02:00:02PM -0700, Aaron Blosser wrote:
>>I fear that many folks may not be aware of the list, or find
>>that subscribing seems too hard (odd as that may sound to us experts :)
>
>Or perhaps being set back by the description of an "in-depth discussion
>about Mersenne primes"... ;-) When people start throwing the maths
>around, I feel like I should take more maths soon :-P
I'd tend to agree - the list is, at times, too in-depth for my
understanding, though it's lead me to do a fair amount of research on
my own. There are still discussions about CPU architecture, as well
as off-topic discussions about systems adminstration, that I don't
pretend to follow, but I've found that I've learned a lot reading
through those discussions.
As for a 'users' mailing list, I don't feel that that's necessary; if
'ordinary users' want to get on the list, they can simply read only
those threads that they understand and are interested in. The list
isn't so high-volume as to make that in any way prohibitive.
Nathan
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Date: Tue, 15 May 2001 16:48:14 +0100
From: "Kevin Edge" <[EMAIL PROTECTED]>
Subject: Mersenne: Yeti at Home
You may be interested (briefly) in a new distributed computing
project that I have come across - Yeti at Home. Details at:
http://www.phobe.com/yeti/index.html
Kevin Edge
{:<)}
- -----------------------------------
Kevin Edge - [EMAIL PROTECTED]
- -----------------------------------
The opinions herein are my own and,
unless explicitly stated,
may not represent those of
Northgate Information Systems
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------------------------------
Date: Tue, 15 May 2001 18:12:39 +0200
From: Paul Landon <[EMAIL PROTECTED]>
Subject: Re: Mersenne: games one can play with genuine composites
If a prime Q | M_C
then Order(2,Q) | C ;but not 1
Order(2,Q) | Q-1
F:=GCD(C,Q-1) != 1
F will either be C or one of it's divisors.
If Order(2,Q)==C then it has almost zero information
to tell us anything about the factors of C.
If C has 2 factors P0 & P1 then the product of factors
with Order == C is M_C/(M_P0.M_P1)
with Order == P1 is M_P1
Order == P0 is M_P0
(For more than 2 factors of C, Pofwo(C) is recursively
defined as M_C / all the pofwos of the divisors of C).
I would expect the probability that a factor of M_C
has these orders to be a non-decreasing function of these
products.
An approximation for the probabilities could be just the
ratio of these products.
Sadly for composites such as M727 which guesses have as
having a small number of factors and it is known that the
smallest factor is bigger than a decent bound, F will
equal M727 nearly all the time, and rarely will a factor
be found. There is also the rare case where the order of
Q <= M_C but F=M_C
The distribution of Mersenne Divisors is such that small
Q will tend to have a smaller order, and any Q<=2M_C
will not have order M_C.
If you are only searching for factors of M_C of the form
KC+1 then these will always have F=M_C and tell us nothing
about the factors of C. The only factors of M_C that help
with factoring C are those not of the form KC+1.
Stating the obvious, M_C is exponentially bigger than
C and even a trial divison of M_C using exponentiation
will take longer than meaningful operations on C.
For example a division of M_M727 is not practical, but if
a factor of M_C is found it is worth doing one GCD.
So an approximate heuristic that anyone can better by not
using a geometric mean or using knowledge of the distribution
of Mersenne Divisors, is that for C having 2 factors, the
probability of Q | M_C helping with factoring C is approx:-
M_P0 + M_P1
- -----------------------
M_C + M_P0 + M_P1
- ---------
M_P0.M_P1 or not a lot!
Cheers,
Paul Landon
ps. Every train driver knows that Scottish sheep have
a maximum of 7 colours :-)
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Date: Tue, 15 May 2001 16:33:28 +0100
From: "Daran" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Re: 26 exponents
- -----Original Message-----
From: Jud McCranie <[EMAIL PROTECTED]>
To: [EMAIL PROTECTED] <[EMAIL PROTECTED]>
Date: 15 May 2001 04:52
Subject: Re: Mersenne: Re: 26 exponents
>Well, how about this - new users can get an exponent that has been
>abandoned several times, but they must check in at least once a month to
>report the percentage done and expected completion date to show that they
>are making reasonable progress. It could even be automatic. Or maybe check
>in at 1 month, 2 months after that, and then every three months? Or is
>that too elitist too?
No, It's just too complicated.
Regards
Daran
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Date: Tue, 15 May 2001 16:34:50 +0100
From: "Daran" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Re: 26 exponents
- -----Original Message-----
From: Jud McCranie <[EMAIL PROTECTED]>
To: [EMAIL PROTECTED] <[EMAIL PROTECTED]>
Date: 15 May 2001 04:34
Subject: Re: Mersenne: Re: 26 exponents
>At 09:44 PM 5/14/2001 -0400, Nathan Russell wrote:
>They would still be contributing towards milestones. If there are
>exponents below a milestone that never have been assigned, they would get
>them.
Are there any exponents below #38 that have never been assigned?
[...]
>But there could be one smaller than what now seems to be #38, because there
>are exponents in that range that haven't had even 1 LL.
I'm not adept at the number theory, but presumably these are more likely to be
prime for no other reason than because they are relatively small, and the
density of Mersenne primes decreases with size.
>| Jud McCranie |
Daran G.
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Date: Tue, 15 May 2001 16:38:40 +0100
From: "Daran" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Re: 26 exponents
- -----Original Message-----
From: Nathan Russell <[EMAIL PROTECTED]>
To: [EMAIL PROTECTED] <[EMAIL PROTECTED]>
Date: 14 May 2001 14:31
Subject: Re: Mersenne: Re: 26 exponents
>On Mon, 14 May 2001 00:20:47 +0100, Daran wrote:
>
>>As someone currently running a legacy machine, (It's taking 4-5 months to
run
>>double-checks in the range under consideration,) I have some thoughts on
this.
>>
>>First of all, as Jud notes, the 'elitism' is already there, in that
different
>>machines get treated differently in the assignments that they are given. It
>>also lies at the heart of the 'Top producer' chart.
>
>Every distributed computing project larger than a few dozen members
>has such a chart. It would be difficult to keep people interested
>without one. I know that I don't feel less a part of the project
>because my placing is above 4,000.
I daren't look at my placing, but I'm pretty sure I'm going backwards. :-)
>>Even readers of this list
>>get opportunities to acquire exponents or prebeta-test software, etc., that
>>are not available to the unwashed masses.
>
>Very true. Of course, George can hardly contact all several thousand
>participants when such an opportunity happens.
As I said, the intention is not to criticise current practice, but to point at
that there is already differential treatment between participants, and that it
really isn't something to worry about, IMO.
[...]
>>If I choose to specify what kind of work I want, I
>>still expect the be given the work that "makes most sense" within that
>>category. I certainly would not expect to be given work that would delay a
>>milestone, given the limitations of my machine.
>
>This might be a reasonable change in PrimeNet. Personally, I don't
>think milestones should be a focus of the project, but it is nice when
>a new one appears on the page.
True. Similarly top producer ranking isn't a focus of the project, but it's
nice (or not nice, in my case) to see how well you're doing.
[...]
>I still think that this is very debatable. There should not be a
>certain /assignment type/ reserved for 'veterans', but it may be
>reasonable to, e.g., only give triple-checks to accounts that request
>double-checks, and have returned more than a certain number of
>results.
In what way is that not reserving an assignment type - triple-checks - to
veterans?
>>People need to be informed about
>>departures from documented practice.
>
>Are you suggesting that, every time George offers exponents to the
>members of this mailing list, he should send out a newsletter to every
>participant - guaranteeing hundreds or thousands of replies for him to
>deal with? I think there may be no good solution to this.
No, of course not. I meant changes in practise that affect /them/. For
example the suggestion that an exponent be assigned to two people
simultaneously, with the first one back counting as the primary test, and the
second as the double-check. If I asked for a first-time check (or if I
thought I had been given one), then I should not be happy if I found out later
that someone else had gotten there first..
>Nathan
Daran G.
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Date: Tue, 15 May 2001 16:35:42 +0100
From: "Daran" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Re: 26 exponents
- -----Original Message-----
From: Nathan Russell <[EMAIL PROTECTED]>
To: Brian J. Beesley <[EMAIL PROTECTED]>; [EMAIL PROTECTED]
<[EMAIL PROTECTED]>
Date: 15 May 2001 03:26
Subject: Re: Mersenne: Re: 26 exponents
>Agreed. Membership to the list indicates a slightly-more-than-casual
>interest in the project, specifically a willingness to sift through a
>few dozen messages per month in order to learn more about the project.
>That interest might well also be a sign of someone who is more likely
>to faithfully complete 'special' assignments in a relatively timely
>fashion.
I'm sure it is. My intention wasn't to criticise the practice. It just seems
absurd to me to worry about 'elitism' in the choice of actual exponent
assigned, which the user isn't going to be aware of anyway, and then to be
content with the 'elitism' in the 'most sense' choice of test type, or in the
additional opportunities afforded to list members. I put 'elitism' into
quotes because I don't agree that it is elitism at all.
>Nathan Russell
Daran G.
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Date: Tue, 15 May 2001 16:36:20 +0100
From: "Daran" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: missing exponents?
- -----Original Message-----
From: Nathan Russell <[EMAIL PROTECTED]>
To: [EMAIL PROTECTED] <[EMAIL PROTECTED]>
Date: 15 May 2001 03:25
Subject: Re: Mersenne: missing exponents?
>I have version 20.6.1 - and the web page reads that all versions were
>last updated June 15 2000. Something odd is going on...
That's the version I'm running. Has there been an update since last June that
I don't know about?
>Nathan
Daran G.
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Date: Tue, 15 May 2001 16:48:19 +0100
From: "Daran" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Re: 26 exponents
- -----Original Message-----
From: Steve <[EMAIL PROTECTED]>
To: [EMAIL PROTECTED] <[EMAIL PROTECTED]>
Date: 14 May 2001 07:59
Subject: Re: Mersenne: Re: 26 exponents
>That _might_ be a good idea, except in the eventual situation where both
>participants return results indicating their number is indeed prime. Whoever
>had the slightly slower machine will not be very happy!
That gets my vote for understatement-of-the-year. :-)
BTW what happens now when a first-time check, (or for that matter, if a
double-check) discovers a new prime. Surely this is checked immediately on
the fastest machine available to the project, and not left to the vagaries of
random allocation?
>Steve Harris
Daran G.
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Date: Tue, 15 May 2001 16:49:02 +0100
From: "Daran" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Re: 26 exponents
- -----Original Message-----
From: Nathan Russell <[EMAIL PROTECTED]>
To: [EMAIL PROTECTED] <[EMAIL PROTECTED]>
Date: 13 May 2001 02:58
Subject: Re: Mersenne: Re: 26 exponents
>On Sat, 12 May 2001 18:21:17 -0400, Jud McCranie wrote:
>There would still be a distinction drawn between 'new' and
>'experienced' users, and I think drawing any such distinction would
>make new users feel less valued - and quite possibly lead them to join
>one of the other fairly large projects, all of which are completely,
>or nearly completely, automated.
Why should there be any less automation if multiply expired exponents are only
awarded to fast machines with a track record of reliability?
Alternatively, since nobody seems to find it objectionable, why not take these
exponents off the primmest server, and offer them to list subscribers only?
>Nathan
Daran G.
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Date: Tue, 15 May 2001 18:22:19 +0100
From: "Daran" <[EMAIL PROTECTED]>
Subject: Mersenne: GIMPS accelerator?
I know very little about computer architecture, so please feel free to shoot
me down if what follow is complete nonsense.
GIMPS clients use the spare capacity of the primary processing resource within
any computer:- the CPU(s). But most modern PCs have another component capable
of performing rapid and sophisticated calculations:- the GPU on the graphics
accelerator. Is there any way that the GPU can be programmed to perform GIMPS
processing when otherwise not in use? If this could be done, then it would
have the effect of turning every client computer into an multi-processor
system.
Regards
Daran G.
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Date: Tue, 15 May 2001 11:20:07 -0700
From: Eric Hahn <[EMAIL PROTECTED]>
Subject: Mersenne: ECM Question...
I think I know the answer to this question, but am asking it...
just to make sure...
According to ECMNet, to find factors of up to 25 digits, the
optimal B1 is 50,000 with 300 expected curves... and to find
factors of up to 30 digits the optimal B1 is 250,000 with 700
expected curves...
If a person runs an ECM test using a B1 of 250,000 with 700
curves (for up to 30 digits), will they also find any factors
that they would have found if they had used a B1 of 50,000 with
300 curves (for up to 25 digits) ?!?
Eric
I'm presuming the answer is yes... and it works the same for
each level... (1,000,000 with 1800 expected curves for up to 35
digits, etc.)...
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Date: Tue, 15 May 2001 11:54:32 -0700
From: "John R Pierce" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: GIMPS accelerator?
> I know very little about computer architecture, so please feel free to
shoot
> me down if what follow is complete nonsense.
>
> GIMPS clients use the spare capacity of the primary processing resource
within
> any computer:- the CPU(s). But most modern PCs have another component
capable
> of performing rapid and sophisticated calculations:- the GPU on the
graphics
> accelerator. Is there any way that the GPU can be programmed to perform
GIMPS
> processing when otherwise not in use? If this could be done, then it
would
> have the effect of turning every client computer into an multi-processor
> system.
Virtually all GPU's in use today are fixed function hard wired graphics
accelerators. There's no way to use them for general purpose computational
use. Also, there's no APIs, and each chip vendor has a radically different
architecture.
- -jrp
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Date: Tue, 15 May 2001 15:11:40 -0400
From: Jud McCranie <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Re: 26 exponents
At 04:34 PM 5/15/2001 +0100, Daran wrote:
>Are there any exponents below #38 that have never been assigned?
Not as far as I know, but there are over 20 that haven't had the first LL
test completed. But they should have all been assigned at least 24 months
ago.
+------------------------------------+
| Jud McCranie |
| |
| former temporary part-time adjunct |
| instructor of a minor university |
+------------------------------------+
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Date: Tue, 15 May 2001 15:54:33 -0400
From: George Woltman <[EMAIL PROTECTED]>
Subject: Mersenne: P4 executable
Hi all,
I've uploaded a version that fixes 2 bugs in the new P4 prime95.
1) Trial factoring was broken. In switching to MASM 6.15, an assembler
bug caused the factoring code to blow up.
2) I restored a FPU init instruction that I accidentally deleted. This caused
the excessive round-off errors when running the old FFT code.
Again, *FOR P4 USERS ONLY* the fixed version is at
ftp://mersenne.org/gimps/p95v21a.zip
Have fun,
George
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Date: Tue, 15 May 2001 22:36:55 +0200
From: "Steinar H. Gunderson" <[EMAIL PROTECTED]>
Subject: Mersenne: Re: 26 exponents
On Tue, May 15, 2001 at 04:48:19PM +0100, Daran wrote:
>BTW what happens now when a first-time check, (or for that matter, if a
>double-check) discovers a new prime. Surely this is checked immediately on
>the fastest machine available to the project, and not left to the vagaries of
>random allocation?
It is run on a different architecture, with different software. The
three first were (as far as I know) tested on Crays, while the 4th (M38
(we think)) was tested on an Alpha machine with mlucas, as far as I
remember.
The idea is to completely eliminate any possibility of a persistent
program or hardware bug :-)
/* Steinar */
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Date: Tue, 15 May 2001 13:46:03 -0700 (PDT)
From: James Escamilla <[EMAIL PROTECTED]>
Subject: Re: Mersenne: GIMPS accelerator?
- --- Daran <[EMAIL PROTECTED]> wrote:
> I know very little about computer architecture, so please feel free
> to shoot
> me down if what follow is complete nonsense.
>
> GIMPS clients use the spare capacity of the primary processing
> resource within
> any computer:- the CPU(s). But most modern PCs have another
> component capable
> of performing rapid and sophisticated calculations:- the GPU on the
> graphics
> accelerator. Is there any way that the GPU can be programmed to
> perform GIMPS
> processing when otherwise not in use? If this could be done, then it
> would
> have the effect of turning every client computer into an
> multi-processor
> system.
>
> Regards
>
> Daran G.
>
>
>
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Date: Tue, 15 May 2001 23:06:36 +0100
From: Gareth Randall <[EMAIL PROTECTED]>
Subject: Re: Mersenne: GIMPS accelerator?
Daran,
This is an interesting piece of lateral thinking that deserves to go further than I
think it actually does.
Essentially, I'm not sure how the operations that a graphics card can provide, such as
line drawing, texture overlaying, raytraced light effects etc, could be made to
implement a LL test or FFT etc which would require things like bit tests, conditioning
branches and loops etc.
Conceivably additions could be done by superimposing textures and reading back the
resulting frame buffer, but these wouldn't be 64-bit precision additions! Maybe some
form of matrix multiplication could be done by rotating textures before superimposing?
However, I think the resulting calculation efficiency would be very poor, and may
never achieve useful precision.
Also, any code would be very hardware specific, and may only work if the display was
not displaying, say, a desktop.
However, if someone could implement it, it could provide the *ultimate* in Mersenne
related screen savers! What you'd see on the screen would be the actual calculations
themselves taking place before your eyes, and with no overheads for displaying it
either!
Yours,
======= Gareth Randall =======
Daran wrote:
>
> I know very little about computer architecture, so please feel free to shoot
> me down if what follow is complete nonsense.
>
> GIMPS clients use the spare capacity of the primary processing resource within
> any computer:- the CPU(s). But most modern PCs have another component capable
> of performing rapid and sophisticated calculations:- the GPU on the graphics
> accelerator. Is there any way that the GPU can be programmed to perform GIMPS
> processing when otherwise not in use? If this could be done, then it would
> have the effect of turning every client computer into an multi-processor
> system.
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Date: Tue, 15 May 2001 22:23:33 -0000
From: "Brian J. Beesley" <[EMAIL PROTECTED]>
Subject: Re: Overriding assigned exponent type (was Re: Mersenne: Re: 26 exponents)
On 14 May 2001, at 23:33, Steinar H. Gunderson wrote:
> Or perhaps being set back by the description of an "in-depth discussion
> about Mersenne primes"... ;-) When people start throwing the maths
> around, I feel like I should take more maths soon :-P
>
> Anyhow, no critique, but perhaps this _isn't_ a mailing list for the
> general user. I personally like it, but the average SETI@Home `convert'
> might not. Perhaps we could have a general `users' list instead?
If you understand _nothing_ discussed on a mailing list, there's no
point in subscribing. Similarly if you understand _everything_. You
can always delete the messages which you consider beyond your
intellect, or beneath contempt. Personally I like the range we have
at present.
Some of the deeper maths makes me go away & read up on the topic, &
occasionally I get a bit wiser as a result.
The usual problem with splitting a mailing list into "experts" &
"novices" lists is that the "novices" list dies out for lack of any
"expert" content. I don't think splitting this list would work unless
the "novices" list was actively managed by a few of us who do have
reasonable experience.
Regards
Brian Beesley
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Date: Tue, 15 May 2001 22:23:33 -0000
From: "Brian J. Beesley" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Purpose of the self-test; also, aren't P4s fast!
On 14 May 2001, at 20:52, George Woltman wrote:
>
> >Is the self-test in fact just to check
> >that there's not something in the CPU which goes glitchy when running
> >flat-out SSE2 code for hours on end?
>
> Yes. The QA suite that Ken Kriesel and Brian Beesley worked on does a
> better job at testing edge conditions. Of course, they'll need to update that
> suite using the new limits.
>
Presumably FPU code on processors other than the P4. But yes, it is
and (to the best of my knowledge) always has been a hardware test
rather than a test of the software, at any rate once the software is
in the hands of users.
Actually most of the exponents in the test suite were chosen to
exercise code in a manner which is particularly hard on the "magic
numbers" involved in the collapsed DWT. I'm sure we can find some
more exponents & extend the test suite so that more candidates are
available in the appropriate range for each FFT run length. Probably
this was getting overdue anyway, given the increasing performance of
available processors.
Perhaps it would help us if George could indicate the approximate
limits for each run length when the SSE2 code is in use.
But could I just point out that there is a _potential_ benefit in
running selftests using ridiculously small exponents for the run
length being tested. Normally the maximum permitted roundoff error is
0.4; this means that a roundoff error will only be detected as such
on one in every five occasions on which it occurs. If we use a small
exponent then we could reduce the roundoff error limit to 0.1 (or
maybe even less) and therefore detect a much larger proportion of any
roundoff errors which might occur. The fact that the residual checked
at the end of each self-test may still be correct does not prove that
a hardware glitch has not occurred, though gross errors will of
course cause the selftest to fail for this reason.
If this idea is developed, it's important to be aware that using too
small an exponent for a particular run length can invalidate the
"subtract two" coding in the LL test. I think the lower limit is
three bits per element, though this may depend to some extent on the
exact way in which the code is implemented.
Regards
Brian Beesley
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Date: Tue, 15 May 2001 22:23:33 -0000
From: "Brian J. Beesley" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Re: 26 exponents
On 14 May 2001, at 21:56, Nathan Russell wrote:
> otherwise, you might
> have someone using a 486 suddenly realize that their computer was
> doing a first-time check that would take over a year, get frustrated,
> and give up.
A first-time check on a 10M exponent would take _several_ years on a
486!
Actually I think that there may be a perceptual problem with many new
users in that they may give up as soon as they realize that a "most
sense" assignment is going to take several weeks to complete.
Unfortunately there seems to be no easy way to fix this!
>
> >There is also a theoretical difference between those exponents
> >congruent to 1 modulo 4 and those congruent to 3 modulo 4. However I
> >believe that this is due to the fact that one of these groups has a
> >larger probability of having a small factor; thus this irregularity
> >is removed by the time that LL testing begins.
>
> I think I read something similiar. Might it relate to whether the
> first potential factor itself is prime, specifically whether it is
> divisible by 3? I can't do the arithmetic in my head, but I have a
> hunch...
Um. 2p+1 = 3 mod 4 irrespective of whether p = 1 mod 4 or p = 3 mod 4
However for "large" p there doesn't seem to be any link to
divisibility of 2p+1 by 3, or any other "small" prime.
The obvious bias against 3 mod 4 exponents is that those which are
Sophie-Germain primes are guaranteed to be divisible by 2p+1.
We can also examine 2kp+1 mod 8, which must be 1 or 7 if it is a
candidate factor of M(p).
When p = 1 mod 4, p = 1 mod 8 or p = 5 mod 8, so 2p = 2 mod 8,
therefore:
2p+1 = 3 mod 8, so can't be a factor
4p+1 = 5 mod 8, so can't be a factor
6p+1 = 7 mod 8, so might be a factor
8p+1 = 1 mod 8, so might be a factor
...
so the values of k which checking are 3, 4, 7, 8, 11, 12, ...
When p = 3 mod 4, p = 3 mod 8 or p = 7 mod 8, so 2p = 6 mod 8,
therefore
2p+1 = 7 mod 8, so might be a factor
4p+1 = 5 mod 8, so can't be a factor
6p+1 = 3 mod 8, so can't be a factor
8p+1 = 1 mod 8, so might be a factor
...
so the values of k which need checking are 1, 4, 5, 8, 9, 12, ...
The multiples of 4 are common to both series, but the other possible
k values are smaller in the p = 3 mod 4 series than those in the
p = 1 mod 4 series. And, other things being equal, smaller k values
are in general more likely to be provide a factor than larger ones.
However, trial factoring to k >> 10^6 surely reduces the difference
to a miniscule amount.
> Perhaps clicking the 'give me the work that makes the most sense' box
> should immediately set the appearance of the others to the work that
> will be chosen, rather than simply graying them out.
Agreed.
Regards
Brian Beesley
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Date: Tue, 15 May 2001 16:02:06 -0700 (PDT)
From: James Escamilla <[EMAIL PROTECTED]>
Subject: Re: Mersenne: GIMPS accelerator?
We currently use the FPU (floating point unit) which most office
software doesn't use. The GPU is hard coded for graphics and not
really useful for anything else.
- --- Daran <[EMAIL PROTECTED]> wrote:
> I know very little about computer architecture, so please feel free
> to shoot
> me down if what follow is complete nonsense.
>
> GIMPS clients use the spare capacity of the primary processing
> resource within
> any computer:- the CPU(s). But most modern PCs have another
> component capable
> of performing rapid and sophisticated calculations:- the GPU on the
> graphics
> accelerator. Is there any way that the GPU can be programmed to
> perform GIMPS
> processing when otherwise not in use? If this could be done, then it
> would
> have the effect of turning every client computer into an
> multi-processor
> system.
>
> Regards
>
> Daran G.
>
>
>
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Date: Wed, 16 May 2001 01:40:53 +0200
From: "Steinar H. Gunderson" <[EMAIL PROTECTED]>
Subject: Re: Overriding assigned exponent type (was Re: Mersenne: Re: 26 exponents)
On Tue, May 15, 2001 at 10:23:33PM -0000, Brian J. Beesley wrote:
>If you understand _nothing_ discussed on a mailing list, there's no
>point in subscribing. Similarly if you understand _everything_. You
>can always delete the messages which you consider beyond your
>intellect, or beneath contempt. Personally I like the range we have
>at present.
Yes -- that is my opinion too. I skim quite a lot, though ;-)
>Some of the deeper maths makes me go away & read up on the topic, &
>occasionally I get a bit wiser as a result.
Hmmm, I think I've learned quite a bit of maths just be skimming :-)
It's surprising how much you can learn just by looking at a clueful
calculation, even if you don't really understand the maths behind it.
Now, just to print out my maths hand-in where one of the proofs utilizes
(simple!) modular arithmetic, which I've learned... here. :-) (We haven't
had it in school yet, but I suppose we will next year.)
(If anybody wants to know, it's `prove that n^3 - n has 24 as a factor,
for odd n' :-) )
/* Steinar */
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Date: Tue, 15 May 2001 19:58:06 -0400
From: Jud McCranie <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Re: 26 exponents
At 10:23 PM 5/15/2001 +0000, Brian J. Beesley wrote:
>Actually I think that there may be a perceptual problem with many new
>users in that they may give up as soon as they realize that a "most
>sense" assignment is going to take several weeks to complete.
>Unfortunately there seems to be no easy way to fix this!
How about a warning beforehand? Over 18,000 people have completed at least
one assignment. Are the any figures for how many started, and then never
finished?
+-------------------------------------------------+
| Jud McCranie |
| |
| You'll never need more than 640 megs of memory. |
+-------------------------------------------------+
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Date: Wed, 16 May 2001 01:40:16 +0100
From: Steve <[EMAIL PROTECTED]>
Subject: Mersenne: Primestats perl script updated, (bug fix).
Hi All
I've noticed that sometimes the topproducers table goes a bit
strange, this causes the primestats script to output 2 Meg worth
of error messages, not good if you run it in a cron job, and then
the cron job backs up your inbox.
So I've tracked the bug down and fixed it so now you only get 24
lines of error message when we have a problem with topproducers.shtml
rather than 2 Megs worth.
It's here: http://www.zeropps.uklinux.net/linstuff.html
- --
Cheers
Steve email mailto:[EMAIL PROTECTED]
%HAV-A-NICEDAY Error not enough coffee 0 pps.
web http://www.zeropps.uklinux.net/
or http://start.at/zero-pps
1:35am up 103 days, 2:22, 2 users, load average: 1.03, 1.08, 1.11
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Date: Tue, 15 May 2001 20:46:58 -0400
From: Nathan Russell <[EMAIL PROTECTED]>
Subject: Mersenne: SUMOUT errors
In the course of a single P-1 run, I've gotten 3 SUMOUT errors:
[Tue May 15 08:20:24 2001]
SUMOUT error occurred.
[Tue May 15 12:04:41 2001]
SUMOUT error occurred.
[Tue May 15 20:05:15 2001]
SUMOUT error occurred.
In the past fifteen months with GIMPS, I had gotten only two errors.
I can't help wondering if this could have something to do with a
corrupt Win98 swapfile, since all of the errors occured during Stage
2; however, I would think that that would have caused far more errors.
Additionally, I've only had one system
I'll run a thorough Scandisk tonight. I don't know if CPU overheating
might be a problem, since I just moved the machine home and it's about
70-75 Farenheit here during the day. The machine 'sounds' exactly the
same, and since I have Asperger's Syndrome (a mild form of autism) I
tend to trust my sense of hearing implicitely. That said, if there's
a hardware problem of some sort, I'd want to have it checked out very
promptly!
The major changes in the past several days:
1. I am now using my modem rather than my ethernet card.
2. As said above, i'm home, and it's warmer (though the machine has
operated in an environment that was warmer still this past August).
Also, when I put my hand at the vent, it barely feels luke-warm - and
it felt hot to the point of being uncomfortable before.
3. The machine was transported about 70 miles, and might have been
somehow jolted - but appears to work fine.
4. All three errors occured during P-1 Stage 2, and I specifically
remember that the machine was swapping fairly heavily at the time of
the first and second errors (I had stopped back to check email). I'll
reduce the allowed memory by 10 megs or so when this run is over.
5. I was using my software modem at those times - but not at the time
of the third error, and I'd used it without trouble earlier this
weekend, but not during heavy swapping.
Any insight would be appreciated. I've never had stability problems
before. I'll be more concerned if they continue when this P-1 run is
over, at about midnight.
Regards,
Nathan
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End of Mersenne Digest V1 #852
******************************
