Mersenne Digest Thursday, July 29 1999 Volume 01 : Number 606
----------------------------------------------------------------------
Date: Thu, 29 Jul 1999 00:59:55 -0500 (CDT)
From: [EMAIL PROTECTED]
Subject: Mersenne: Fermat Number F24
In response to the message from...
From: Yann Forget <[EMAIL PROTECTED]>
Subject: Mersenne: Fermat number & others
Hi,
I have a few questions which are not in the FAQ :
- - - What about testing F24 with Pepin's test ?
(http://www.utm.edu/research/primes/glossary/PepinsTest.html)
Is there a code for this ? On Intel (MS Windows or Linux) ?
Is there some machine running this ?
How long would it take to test the primality of F24 with a PII (for ex.)
- -------------[end of quoted portion of message]----------------
Fermat number F24 has been discussed on the list before, quite a while ago. I think
testing F24
by Pepin's test would take about the same amount of computation as an LL test of a
Mersenne
number with an exponent of about 2^24 (16777216). Based on how long it takes to do an
LL test
with prime95, I would estimate that testing F24 with a PII would take perhaps 6 months
to a
year. A lot depends on how fast the multi-precision arithmetic routines are, of
course. I am
not aware of any existing software for this that is readily available, but writing
one's own
program using existing "big number" arithmetic routines shouldn't be very difficult.
Actually,
it seems quite probable that someone, somewhere, is already in the process of testing
F24. (No,
I don't have any details -- it just seems likely.)
And, no I am not testing F24. Instead, I am trying to figure out how to find a factor
of F14.
- --Jim Howell
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------------------------------
Date: Wed, 28 Jul 1999 23:36:23 -0700
From: Greg Hewgill <[EMAIL PROTECTED]>
Subject: Mersenne: Better to wait?
No doubt you've all heard about the paradox of Man's first interstellar voyage.
If we were to build and launch a spaceship today that would take us to the
nearest star in, say, 100 years, then a better spaceship launched later would
arrive sooner provided our technology advanced fast enough during that time.
When will we reach the crossover point in GIMPS, where it's better to wait for
a faster computer, than to start an LL test today? If we assume that Moore's
Law holds (computing speed doubles every 18 months), then it would seem that
the crossover point would be when an LL test takes 3 years (18*2 months) on
current hardware.
Anybody willing to hazard a guess as to when we'll reach that point?
Greg Hewgill
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------------------------------
Date: Thu, 29 Jul 1999 03:03:18 EDT
From: [EMAIL PROTECTED]
Subject: Mersenne: Merced and Teraprimes
<<Why not? A P90 adds 1 P90 CPU year per year (give or take). Not everyone
can afford a PIII/550.>>
I hope they're at least running P166s by now. What's the average machine a
GIMPSter runs, assuming that the average machine runs 24 hours a day? I
remember it being P181 a while ago, I think.
<<By that time (hopefully) the Intel architecture will be dead.>>
I hope it will be alive, just not x86. The Merced, released in 2000, will
have IA-64 architecture and will _not_ be x86 hardware compatible, only
software compatible (thru emulation). *drool* Any word on if Mr. Woltman
will be coding a Merced version of Prime95?
<<Non-US: million 10^6, milliard 10^9, billion 10^12,
billiard 10^15, trillion 10^18 ...>>
Billiard? Hee hee hee.
<<I'm sensitive and sympathetic to what George & Scott are aiming at,
but I'm coming round to the opinion that the best thing to do is to
go back to the position on the $50K EFF prize - let it be awarded to
the discoverer & trust that some filters back.>>
That's my opinion as well.
<<sorry, it's up to me what i do, they all get done in the end>>
Well, that's _one_ way of looking at it.
<<I have the digests from 383 onwards, I can put them up for download on my
web-site if anyone is interested.>>
That'd be useful. Register it with search engines. :-D
<<Yep, the fame. It's kinda nice to be in demand from radio, tv & press for a
while.>>
Hee hee hee.
<<Prior to this there was a thread October 13-15, 1998>>
Please tell me you looked up that date and didn't memorize it....!
<<Someone will surely poach the exponent before completion>>
Evil! Evil! That.... that.... word! Aiiieee!
<<(The EFF's big money appears to be safe!)>>
Any projections on when we'll find a teraprime? *grin*
S. "I want me a Merced!" L.
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------------------------------
Date: Thu, 29 Jul 1999 09:36:54 -0400
From: "Silverman, Bob" <[EMAIL PROTECTED]>
Subject: Mersenne: RE: Mersenne Digest V1 #605
We can't STOP the EFF from awarding money. But we can't and SHOULDN'T change
any way in which it's being done now, which includes dividing up money in
some Jabibbian manner. In my opinion, as long as _nothing_ changes with
what's being done now, GIMPS isn't really in danger. Jump-aheaders will not
be that much of a problem because testing that large will take a LONG time
with present computers - I think.
** I think the best solution is a simple one. EFF should add the very
simple
requirement that the prize will be awarded to anyone finding the first 10M
digit prime ***using their own code***. They must provide the source code
in
claiming the prize.
** I don't think it fair that some dork gets awarded $100K for being lucky
while using *someone else's code* This takes 0 intelligence.
Hi,
I have a few questions which are not in the FAQ :
- - - What about testing F24 with Pepin's test ?
*** I heard from John Selfridge and several others that such a computation
is
now underway.
- - - Long ago ;-) I made some investigations about the period of inverse of
prime numbers (1/p) (Is this good English ?).
*** Why? The mathematics is simple and well understood and has been known
for centuries. Did you check the literature first, before wasting your
time??
What is it that causes people NOT to do even elementary reading first?
I found an empiric relation between the number of digits of the period
(d) et the fact that p is prime, namely that d is a divisor of p-1. I
have been told that this was proved by Gauss.
*** As, I said, try reading a book on elementary number theory. Look
up "Lagrange's Theorem".
Is there a Web page about this ?
** Does everything have to be on the Web? Have people gotten too lazy to use
a
library?
Is this could be of any use in the search for large primes ?
*** What it is that drives people who clearly have not even done their basic
homework in studying elementary background material to make random, ignorant
speculations? (i.e. "Is this [period length of 1/p] any use in the search
for
large primes?) If you had done basic reading, you would KNOW.
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------------------------------
Date: Thu, 29 Jul 1999 09:17:39 -0500
From: "Griffith, Shaun" <[EMAIL PROTECTED]>
Subject: Mersenne: Billions and Billiards
This message is in MIME format. Since your mail reader does not understand
this format, some or all of this message may not be legible.
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charset="iso-8859-1"
>US: million 10^6, billion 10^9, trillion 10^12 ...
>
>Non-US: million 10^6, milliard 10^9, billion 10^12,
> billiard 10^15, trillion 10^18 ...
That's why a billiard table is so big!
- ------_=_NextPart_001_01BED9CD.1DA3974A
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charset="iso-8859-1"
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN">
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<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1">
<META NAME="Generator" CONTENT="MS Exchange Server version 5.5.2448.0">
<TITLE>Billions and Billiards</TITLE>
</HEAD>
<BODY>
<P><FONT SIZE=2 FACE="Courier New">></FONT><FONT SIZE=2 FACE="Courier New">US:
million 10^6, billion 10^9, trillion 10^12 ...</FONT>
<BR><FONT SIZE=2 FACE="Courier New">></FONT>
<BR><FONT SIZE=2 FACE="Courier New">></FONT><FONT SIZE=2 FACE="Courier New">Non-US:
million 10^6, milliard 10^9, billion 10^12,</FONT>
<BR><FONT SIZE=2 FACE="Courier New">></FONT><FONT SIZE=2 FACE="Courier New">
billiard 10^15, trillion 10^18 ...</FONT>
</P>
<P><FONT SIZE=2 FACE="Courier New">That's why a billiard table is so big!</FONT>
</P>
</BODY>
</HTML>
- ------_=_NextPart_001_01BED9CD.1DA3974A--
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------------------------------
Date: Thu, 29 Jul 1999 08:20:31 -0600
From: "Aaron Blosser" <[EMAIL PROTECTED]>
Subject: RE: Mersenne: Better to wait?
> No doubt you've all heard about the paradox of Man's first
> interstellar voyage.
> If we were to build and launch a spaceship today that would take us to the
> nearest star in, say, 100 years, then a better spaceship launched
> later would
> arrive sooner provided our technology advanced fast enough during
> that time.
>
> When will we reach the crossover point in GIMPS, where it's
> better to wait for
> a faster computer, than to start an LL test today? If we assume
> that Moore's
> Law holds (computing speed doubles every 18 months), then it
> would seem that
> the crossover point would be when an LL test takes 3 years (18*2
> months) on
> current hardware.
>
> Anybody willing to hazard a guess as to when we'll reach that point?
It doesn't really matter when we reach that point, IMO.
We can start testing bigger numbers on existing machines and then simply
transfer that over to our new, faster machines when they become available.
It doesn't really compare to the spaceship analogy, unless this guy built
his own faster spaceship along the way and then finished up in that one
instead.
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------------------------------
Date: Thu, 29 Jul 1999 08:25:39 -0600
From: "Aaron Blosser" <[EMAIL PROTECTED]>
Subject: RE: Mersenne: Merced and Teraprimes
> <<Why not? A P90 adds 1 P90 CPU year per year (give or take).
> Not everyone
> can afford a PIII/550.>>
>
> I hope they're at least running P166s by now. What's the average
> machine a
> GIMPSter runs, assuming that the average machine runs 24 hours a day? I
> remember it being P181 a while ago, I think.
Of course the last time we got into this (poaching thread) we learned that
there are people out there who insist on running first time LL tests on
P-60's and what not. :-(
> <<By that time (hopefully) the Intel architecture will be dead.>>
>
> I hope it will be alive, just not x86. The Merced, released in 2000, will
> have IA-64 architecture and will _not_ be x86 hardware compatible, only
> software compatible (thru emulation). *drool* Any word on if
> Mr. Woltman
> will be coding a Merced version of Prime95?
If he doesn't, someone will.
> <<Non-US: million 10^6, milliard 10^9, billion 10^12,
> billiard 10^15, trillion 10^18 ...>>
>
> Billiard? Hee hee hee.
Think about it. Billiards = 15 balls (not counting cue)...ahh..it all makes
sense now! :-)
> <<Yep, the fame. It's kinda nice to be in demand from radio, tv &
> press for a
> while.>>
>
> Hee hee hee.
Of course, this all depends on "why" the media is trying to get a hold of
you.
> S. "I want me a Merced!" L.
Hehe...I'm going to the Compaq ASE conference in August and I'm sure Intel
will have their own "you gotta sign this NDA" suite again. With any luck,
they'll have one of their Merced prototypes and I can bug them to death on
the details.
Aaron
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------------------------------
Date: Thu, 29 Jul 1999 08:32:11 -0600
From: "Aaron Blosser" <[EMAIL PROTECTED]>
Subject: RE: Mersenne: RE: Mersenne Digest V1 #605
> ** I think the best solution is a simple one. EFF should add the very
> simple
> requirement that the prize will be awarded to anyone finding the first 10M
> digit prime ***using their own code***. They must provide the source code
> in
> claiming the prize.
But that just begs the question of "okay, who *does* get the rest of the
money?"
The author of the source code? Who is that? George and Scott both borrowed
from other sources with their stuff. Couldn't I just make one minor change
to George's code and then call it my own (by those standards)?
Obviously, that's an extreme, but don't underestimate what people will do
for $100K
> ** I don't think it fair that some dork gets awarded $100K for
> being lucky
> while using *someone else's code* This takes 0 intelligence.
I look at the prize as an added incentive (for those who could care less
about the "purity" of a prime) for someone to "donate" their computer time
for days/weeks/months on end. Sure it's luck, but even using your own code,
it's *still* luck. Having your own code or not has nothing really to do
with it.
I'm glad George lets us all use his program because there is hardly a
handful of others who could've coded something like that and without
George's contribution, does anyone really think we'd be testing exponents in
the 8M range?
My vote, if anyone was keeping count, is still to trust in the honor
system - that any winner will gladly give some of the money to George and
Scott, in recognition of their efforts. But for goodness sake, trying to
"require" that goes well beyond the scope of what GIMPS was setup to do.
Aaron
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------------------------------
Date: Thu, 29 Jul 1999 11:15:32 -0400
From: Marc Getty <[EMAIL PROTECTED]>
Subject: Mersenne: Average Machine Speed
> I hope they're at least running P166s by now. What's the average machine a
> GIMPSter runs, assuming that the average machine runs 24 hours a day? I
> remember it being P181 a while ago, I think.
This brings up a very interesting question, what is the average speed of a
machine participating in GIMPS? Does PrimeNet have more data then the CPU type?
I would assume so. Can we get a breakdown of the average CPU speed of a GIMPS
producer and track this over time to see if we are keeping up with Moore's law?
Can the average machine speed be tracked from previous data? Account for the
growth in the number of participating machines and come up with an average
machine speed from year to year?
- -Marc
Marc Getty [EMAIL PROTECTED]
Department of Dental Informatics, Temple University
http://www.temple.edu/dentistry/di/ 215-707-8192
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------------------------------
Date: Thu, 29 Jul 1999 11:14:53 -0400
From: Jud McCranie <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Better to wait?
At 11:36 PM 7/28/99 -0700, Greg Hewgill wrote:
>No doubt you've all heard about the paradox of Man's first interstellar
>voyage.
>If we were to build and launch a spaceship today that would take us to the
>nearest star in, say, 100 years, then a better spaceship launched later would
>arrive sooner provided our technology advanced fast enough during that time.
You could apply that reasoning to any period in time. Suppose we don't do
it now and wait for faster whatever 10 years. In 10 years, they could say
the same thing and wait another 10 years, etc. You could apply that
reasoning over and over, and never get anything done!
I remember when president Reagan cut out all or almost all of the probes to
other planets. He said that the planets would be around in the
future. Carl Sagan said "the planets will be around for a long time, but
will we?"
+----------------------------------------------+
| Jud "program first and think later" McCranie |
+----------------------------------------------+
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------------------------------
Date: Thu, 29 Jul 1999 11:16:59 -0400
From: Yvan Dutil <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Better to wait?
>When will we reach the crossover point in GIMPS, where it's better to wait
for
>a faster computer, than to start an LL test today? If we assume that Moore's
>Law holds (computing speed doubles every 18 months), then it would seem that
>the crossover point would be when an LL test takes 3 years (18*2 months) on
>current hardware.
>
>Anybody willing to hazard a guess as to when we'll reach that point?
The Moore law is more a doubling each 26 month. Actually the typical
calculation
time is about 2-3 month. A three year computation would meam number in the
over
with N>20 000 000.
I my own opinion we are finishing the number slower than the progression of
the
computer power. Therefore we should never reach this cross-over.
Yvan Dutil
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------------------------------
Date: Thu, 29 Jul 1999 10:24:32 -0500
From: Kipton Moravec <[EMAIL PROTECTED]>
Subject: Mersenne: STOP BASHING PEOPLE WITH SLOWER MACHINES!
Aaron Blosser wrote:
>
> > <<Why not? A P90 adds 1 P90 CPU year per year (give or take).
> > Not everyone
> > can afford a PIII/550.>>
> >
> > I hope they're at least running P166s by now. What's the average
> > machine a
> > GIMPSter runs, assuming that the average machine runs 24 hours a day? I
> > remember it being P181 a while ago, I think.
>
> Of course the last time we got into this (poaching thread) we learned that
> there are people out there who insist on running first time LL tests on
> P-60's and what not. :-(
>
I really get annoyed with remarks like this. I don't think I commented
on the last go around on this subject, but since it popped up again I
feel I must this time.
I have been doing this a lot longer than you have been Aaron, and I am
using a P90, and a P233. For someone to tell me that I CAN'T process
first LL tests and have a chance, (slim as it may be), to find the next
largest prime is total B.S. I am not high on the rankings, because some
of the LL tests were before we had prime net and because I have "only"
two "slower" machines. (They are MY machines and not some corporation's
or university's machines, that I have loaded the software on and am
getting credit for.)
So what if my processor is 20% some percent of the speed of someone
elses? It means he and I are getting 120% more done than he can, by
himself.
GIMPS is a cooperative effort, and frowning on people with shower
machines is not friendly, and not in the spirit of GIMPS. We should be
encouraging people to join the effort to find the next largest prime,
and not discouraging them based on their processor type.
Kip
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------------------------------
Date: Thu, 29 Jul 1999 08:31:30 -0700
From: Greg Hewgill <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Better to wait?
On Thu, Jul 29, 1999 at 08:20:31AM -0600, Aaron Blosser wrote:
> It doesn't really matter when we reach that point, IMO.
No, of course it doesn't matter, it was just a curiosity. The spaceship
equivalent of GIMPS would be to maximize the number of landed spaceships at the
destination. In that case, it's best to start sending them as soon as you can;
who cares how long it takes. :)
Greg Hewgill
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------------------------------
Date: Thu, 29 Jul 1999 10:20:12 -0600
From: "Aaron Blosser" <[EMAIL PROTECTED]>
Subject: Mersenne: RE: STOP BASHING PEOPLE WITH SLOWER MACHINES!
> I have been doing this a lot longer than you have been Aaron, and I am
> using a P90, and a P233. For someone to tell me that I CAN'T process
> first LL tests and have a chance, (slim as it may be), to find the next
> largest prime is total B.S. I am not high on the rankings, because some
> of the LL tests were before we had prime net and because I have "only"
> two "slower" machines. (They are MY machines and not some corporation's
> or university's machines, that I have loaded the software on and am
> getting credit for.)
Yikes! :-)
I've been doing this for a while too (pre-Primenet) and if I recall, at the
time I was using P-100's up to P-133's. Those were fine for exponents in
the 1M-2M range for first time LL tests. I think I began with GIMPS around
December '96 or January '97, so I also have alot of CPU years that are not
reflected in the Primenet stats.
I don't mean to say that you have no chance of finding a prime with a slower
machine. It just takes longer to check an exponent is all. It's that
length of time that I'm referring to, not your chances. I won't go into my
whole opinion on this again...for anyone interested, read the list archives
and you'll see my opinion on this spelled out quite well.
I *know* some people will disagree, so save your breath; realize that I
already know it's controversial and leave it at that.
> GIMPS is a cooperative effort, and frowning on people with shower
> machines is not friendly, and not in the spirit of GIMPS. We should be
> encouraging people to join the effort to find the next largest prime,
> and not discouraging them based on their processor type.
I appreciate every God blessed one of the < P-133's out there, even the
486's. I merely wish they'd focus on double-checking and factoring. Heck,
we're even reaching the point where double-checks on current exponents are
taking several months on P-100's and below...there *will* come a point at
which it no longer makes sense to use these machines even for double-checks.
I know, I know. Every machine in GIMPS is useful. But there is that fine
line where the usefulness is SOOOO minimal as to be nearly worthless. For
instance, ever wonder why there is no GIMPS client for an Apple ][, or for
an 8086 running DOS? Where's the Commodore client? I'm sure there are
millions of those lying in landfills all over. I'd bet 1 million
Commodore's would certainly be of great benefit to GIMPS. :-)
Of course, with the cost of electricity to run all those, you'd actually
SAVE money on power *and* run faster by getting a top of the line machine
anyway. And that's my point. At a certain point, the money you pay for
electricity just isn't worth it anymore. Donate those old machines to a
non-profit, take your generous tax write-off, get a new PC, save electricity
(new CPU's use less power anyway), run more iterations per second, etc.
Some people just hang on longer than others...I'm not criticizing that, I'm
merely asking that you think about doing factoring or double-checks for now.
Aaron
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------------------------------
Date: Thu, 29 Jul 1999 18:39:47 +0100
From: "Brian J. Beesley" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Merced and Teraprimes
On 29 Jul 99, at 3:03, [EMAIL PROTECTED] wrote:
> I hope they're at least running P166s by now.
Well, I'm still running a trio of P100s, as well as a quintet of
PIIs. They're a damn sight better than nothing; running a LL test on
an exponent in the 8 million range would be painful, but not half as
painful as testing a 10 million digit number on a PIII-500!
(Exclamation, not 500 factorial ;-)
> Any word on if Mr. Woltman
> will be coding a Merced version of Prime95?
Intel will have to release the Merced architecture documentation to
developers, and George will have to beg, borrow, steal or maybe even
buy a set of the documentation, and some Merced hardware to practise
on.
> Billiard? Hee hee hee.
Yup, I'm British, the only "billiards" I know is a game played with
two white & one red ball on a "billiards" table (like a large pool
table - interesting enough, it's still called a billiards table, even
when snooker is played on it). American cultural "pollution" has
wiped out the old meaning of "billion" i.e. 10^12, everyone here uses
"billion" meaning 10^9.
> <<(The EFF's big money appears to be safe!)>>
>
> Any projections on when we'll find a teraprime? *grin*
>
> S. "I want me a Merced!" L.
You'll _need_ a Merced, or at least an Alpha - even if someone
manages to speed up the algorithm enough to make starting the
computation worthwhile. Suppose we could get away with storing just
one copy of the work vector - that's > 3.3E12 bits, or 400 GBytes of
memory. Even if you could afford that much RAM, IA32 has only a 4GB
virtual address space.
If no-one improves the algorithm, then I'd _expect_ finding a
teraprime to take about 10^9 times as long as finding a gigaprime.
There are (obviously) 1000 times as many iterations to do, each
iteration will take (a bit more than) 1000 times as long to execute,
and the chance that a single exponent will prove to generate a
Mersenne prime is only 1/1000 as much.
10^9 is about 2^30, so I'd suggest a timeframe estimate of 30 Moore's
Law periods between finding the first gigaprime and finding the first
teraprime. So, something of the order of half a century, assuming
(and it's a _big_ assumption - the laws of physics are hard to work
around) that we really can continue to double speed every 18 to 24
months.
I'm 46 now; I expect to live long enough to see a gigaprime (and
maybe even a 13th human being's footstep on the Moon!), but I very
much doubt I will see a teraprime in my lifetime, unless there is a
major, major advance in the theory.
Regards
Brian Beesley
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------------------------------
Date: Thu, 29 Jul 1999 13:57:18 -0400
From: Pierre Abbat <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Billions and Billiards
On Thu, 29 Jul 1999, Griffith, Shaun wrote:
> >%_>US: million 10^6, billion 10^9, trillion 10^12 ...
> >
> >Non-US: million 10^6, milliard 10^9, billion 10^12,
> > billiard 10^15, trillion 10^18 ...
>
> That's why a billiard table is so big!
If the cue to get in the pool is that long, it's not worth waiting. I'm
outahere!
phma
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Date: Thu, 29 Jul 1999 20:10:54 +0200
From: Sturle Sunde <[EMAIL PROTECTED]>
Subject: Re: Mersenne: STOP BASHING PEOPLE WITH SLOWER MACHINES!
> Aaron Blosser wrote:
>> Of course the last time we got into this (poaching thread) we learned that
>> there are people out there who insist on running first time LL tests on
>> P-60's and what not. :-(
> I really get annoyed with remarks like this. I don't think I commented
> on the last go around on this subject, but since it popped up again I
> feel I must this time.
AOL.
I use almost only relatively slow computers. More than 100 of them. If
they are only 1/5 as fast as what some people think is apropiate, it means
that they can do 100 tests in the same time as an appropiate machine does
5. While a very few people think I should stop using those computers for
testing, I'm no 23 on the GIMPS (not Primenet) top-100 list. (I can't
find this Mr. "Go Away Loosers With Slow Computers" there, but he is
probably working under some pseudonym.)
> So what if my processor is 20% some percent of the speed of someone
> elses? It means he and I are getting 120% more done than he can, by
> himself.
This is the whole point about distributed copmputing -- just the idle-time
on as many as possible slow computers makes one unbeatable speed-monster.
This spring I retired a lot of Indys because there were no exponents left
with FFT size at or below 128KB. (256KB FFT takes many months for each
exponent and a few of the now rather old machines got RAM problems.) 18
of them (less than half) participated in the NFS factoring of M619 (which
should be done in a couple of weeks), and together they became one of the
major contributors. 18 Indys, which were standard low-end workstations
five years ago, are not worthless. They can still outperform a couple of
Pentiums.
- --
Sturle URL: http://www.stud.ifi.uio.no/~sturles/ Er det m}ndag i dag?
~~~~~~ MMF: http://www.alladvantage.com/go.asp?refid=BUP399 - St. URLe
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------------------------------
Date: Thu, 29 Jul 1999 14:36:00 EDT
From: [EMAIL PROTECTED]
Subject: Mersenne: Average Machines
<<This brings up a very interesting question, what is the average speed of a
machine participating in GIMPS? Does PrimeNet have more data then the CPU
type?
I would assume so. Can we get a breakdown of the average CPU speed of a GIMPS
producer and track this over time to see if we are keeping up with Moore's
law?>>
Well, not only are our machines getting faster as people see the light and
upgrade for the good of the project (more likely because their copy of Duke
Quakem 64 won't run on old computers, hee hee), people may be leaving them on
longer/shorter, and we always have new people joining. So GIMPS has the
potential to run past Moore's Law, until a copy of GIMPS is on every computer
in the world! *cackle*
<<Can the average machine speed be tracked from previous data? Account for the
growth in the number of participating machines and come up with an average
machine speed from year to year?>>
One would need access to some sort of logs to do that calculation, but I'll
crunch some numbers I see on entropia.com right now.
<<Mersenne PrimeNet Server 4.0 (Build 4.0.017)
Status Summary Report 29 Jul 1999 18:00 (29 Jul 1999 11:00 Pacific)
------- Aggregate CPU Statistics, P90 Units* -------
Last 7 Days Average Cumulative Today
from 23 Jul 1999 06h from 29 Jul 1999 06h
Test Type CPU yr/day GFLOP/s CPU years CPU yr/day
------------ ---------- ---------- ---------- ----------
Lucas-Lehmer 59.773 719.524 27.914 55.912
Factoring 2.286 27.515 0.858 1.718
---------- ---------- ---------- ----------
TOTALS 62.058 747.039 28.772 57.630
------- Internet CPU and Server Resources -------
Machines Applied on 14033 Accounts Server Synchronization 07 May 1999
08:42
Intel Pentium PII/Pro : 10727 Total exponents merged : 211640
Intel Pentium : 6029 Updated only : 98047
AMD K6 : 1701 Added for testing : 109629
Intel 486 : 345 Retained in IPS cleared list : 4112
Cyrix : 495 Cleared IPS tests removed : 20384
Unspecified type : 3955 GIMPS tests removed / purged : 427
---------------------- -------
TOTAL : 23252 Total Cleared by IPS to date :
104385>>
So, the important things I'll be working with are:
Total machines: 23252. P90 CPU Years/day, 7 day average: 62.058.
However, years/day is an awkward unit to work with, so I'll convert it to P90
days/day (i.e. how many P90s we'd need running at full tilt [constantly on]
to produce the same work). I'll spare you the conversion and say it's
22,666.2 P90s. Let's be stupid and multiply that by 90: 2,039,958 P1s (what
has Intel been smoking?). And now let's bring the actual number of machines
we're running:
23252 * P_MegaHertz = 2,039,958 P1.
Solving, we see that the average GIMPSter runs a machine that is never used
for anything and is left constantly on for 24 hours a day with a P87.74
processor. (Obviously by the machine tabulation above, the average GIMPSter
runs a significantly faster computer, but doesn't leave it on for 24 hours a
day). Eh? This is different than the old figure I remember. However, I
calculated that BEFORE I knew how many computers GIMPS had. So, I'll redo the
calculation based on accounts.
14033 (accounts) * P_MegaHerta = 2,039,958 P1.
Solving here, we see that the average account is equivalent to a single
machine running at full tilt with a P145.37 processor. That's more like it.
If I've had a major brain drain in my calculations, feel free to correct my
error on the list.
S. "I want 2 million P1 processors!" L.
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Date: Thu, 29 Jul 1999 13:15:18 -0600
From: "Aaron Blosser" <[EMAIL PROTECTED]>
Subject: RE: Mersenne: Merced and Teraprimes
> > I hope they're at least running P166s by now.
>
> Well, I'm still running a trio of P100s, as well as a quintet of
> PIIs. They're a damn sight better than nothing; running a LL test on
> an exponent in the 8 million range would be painful, but not half as
> painful as testing a 10 million digit number on a PIII-500!
> (Exclamation, not 500 factorial ;-)
I have quite a few P-166's and they're all doing double-checks (I let
Primenet assign the type of work). I even have a few PPro 200's that are
getting double-checks at the moment since those machines are just busy
enough to make the "rollingaverage" around the 800 or so mark, making it
*seem* like a 160 MHz machine I guess. Oh well, no bother to me.
> > Any word on if Mr. Woltman
> > will be coding a Merced version of Prime95?
>
> Intel will have to release the Merced architecture documentation to
> developers, and George will have to beg, borrow, steal or maybe even
> buy a set of the documentation, and some Merced hardware to practise
> on.
I thought Intel had already released developer info on the Merced, but maybe
they only have the marketing stuff out. Either way, I know that most major
manufacturers have already been given to paper info on the Merced specs,
including electrical info, instruction set, etc. Whether this is public or
not is something else. Like I said, anything I can grab from Intel during
the Compaq conference, I will. If it's not covered by NDA, I'll share what
I can.
> If no-one improves the algorithm, then I'd _expect_ finding a
> teraprime to take about 10^9 times as long as finding a gigaprime.
> There are (obviously) 1000 times as many iterations to do, each
> iteration will take (a bit more than) 1000 times as long to execute,
> and the chance that a single exponent will prove to generate a
> Mersenne prime is only 1/1000 as much.
We're really going to need some factoring code that can do trial factoring
well beyond 2^64, to eliminate as many full LL tests as we can.
What would be a good bit size to trial factor a teradigit prime up to? I
know there's some point in the bell curve to optimize how deep to trial
factor for any given exponent...
> 10^9 is about 2^30, so I'd suggest a timeframe estimate of 30 Moore's
> Law periods between finding the first gigaprime and finding the first
> teraprime. So, something of the order of half a century, assuming
> (and it's a _big_ assumption - the laws of physics are hard to work
> around) that we really can continue to double speed every 18 to 24
> months.
I guess we'll just have to see how relevant the breakthrough's in making
atom width traces and even quantum computers will be to the "real" world.
(to quote: "Reality" is the only word in the language that should always be
used in quotes.)
> I'm 46 now; I expect to live long enough to see a gigaprime (and
> maybe even a 13th human being's footstep on the Moon!), but I very
> much doubt I will see a teraprime in my lifetime, unless there is a
> major, major advance in the theory.
Taking quantum computers to a "real" application might just provide the
paradigm switch you're thinking of, several orders of magnitudes of
improvement *could* be possible in the next, oh...say 25-30 years. Big
"maybe".
Aaron
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------------------------------
Date: Thu, 29 Jul 1999 13:31:13 -0600
From: "Aaron Blosser" <[EMAIL PROTECTED]>
Subject: RE: Mersenne: STOP BASHING PEOPLE WITH SLOWER MACHINES!
> I use almost only relatively slow computers. More than 100 of them. If
> they are only 1/5 as fast as what some people think is apropiate,
> it means
> that they can do 100 tests in the same time as an appropiate machine does
> 5. While a very few people think I should stop using those computers for
> testing, I'm no 23 on the GIMPS (not Primenet) top-100 list. (I can't
> find this Mr. "Go Away Loosers With Slow Computers" there, but he is
> probably working under some pseudonym.)
Egads...I'm not telling *anyone* to NOT use slow computers...I'm
"suggesting" they use < p166 for double-checks or factoring. I do, Primenet
will assign them that way if you let it, it's no big deal when you think
about it. Unless, that is, you're only motivation is prize money in which
case double-checking gets you none in all likelihood. Heck, now that the
$50K prize is gone, nobody is going to get the next prize anytime soon
anyway, so why not do double-checks?
BTW, my Primenet ID is madpoo if anyone is interested (and who would be).
Currently we're oscillating between 20-21 on Primenet. Strangely, I am 220
on the GIMPS list, but my brother Jeremy is 54...I don't know how that
happened since we both use the same madpoo primenet ID...hmmm...does he go
by email or something? As team "madpoo" we have about 4-5 different people
contributing...would we all show up separately in the GIMPS rankings?
Even more curiously, I checked my *old* Primenet ID recently, "blosser" and
lo and behold, what did I find? One of the US WEST machines had turned in a
result as recently as May of this year!! yikes! Looks like they found it
since the current exponenent assigned to that machine is way past due.
If anyone cares to join the mostly extinct team "blosser" the password is
"acidrain" (which the search warrant pages clearly show).
> This spring I retired a lot of Indys because there were no exponents left
> with FFT size at or below 128KB. (256KB FFT takes many months for each
> exponent and a few of the now rather old machines got RAM problems.) 18
> of them (less than half) participated in the NFS factoring of M619 (which
> should be done in a couple of weeks), and together they became one of the
> major contributors. 18 Indys, which were standard low-end workstations
> five years ago, are not worthless. They can still outperform a couple of
> Pentiums.
This is an excellent illustration of my point. Some machines are much
better suited to something *besides* GIMPS, such as the NFS factoring
challenges, or even the DES crackers.
I'd rather see computing power applied to a project with some thought given
to how that computing power can best be used. A 486, with it's rather
pitiful FP performance, should be given something to do that will stick with
integer ops, just for example. It makes little sense to have a 486 doing LL
testing when it would be flexing it's power best by doing factoring.
I hope I'm being clear that I don't consider slower computers useless
entirely...just useless for doing LL tests in the range of exponents
currently being assigned. There are PLENTY of other things they could be
doing that make much more sense, as you have figured out.
Aaron
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End of Mersenne Digest V1 #606
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