Mersenne Digest Tuesday, 2 March 1999 Volume 01 : Number 517
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From: [EMAIL PROTECTED]
Date: Sun, 28 Feb 1999 18:01:27 EST
Subject: Mersenne: Re: Mersenne Digest V1 #515
<<How about sweetening the pot for anyone who is doing double checking
that discovers a mistake in the first LL analysis? >>
Hrm. A small reward would be an incentive. Of course, any mistakes found would
have to be TRIPLE-checked, so that no one fakes an error (easy) to get the
incentive. Of course, anyone who did such a thing would have to be branded a
liar and not allowed to participate in GIMPS any more.
Double-checking finds errors 1/400 of the time, if I remember correctly.
<< But the execution of the instructions themselves are probably about the
same. I have heard that FP speeds would go up some though... Prime95 may run
slower on a Merced at the same clock speed as a Xeon, at least until it's
recompiled. Sigh...>>
The Merced, if I remember correctly, does NOT have native x86 processing
capability, only through emulation. Pentium III Xeons will remain the fastest
processors for x86 instructions. But Prime95 written in Merced assembler....
*begins to drool*
<<Earlier I posted the notion that Mersenne primes might be used to
impress extraterrestrial civilizations. After thinking it thru, I think we
can make a stronger arguement than that: Mersenne primes might
be the *best* yardstick to *prove* a certain level of technological
achievement, perhaps the most logical yardstick.>>
Interesting. I like it. But there is one way that it could be a nonreliable
indicator of technological achievement. If an exoculture receives our Mersenne
prime message, they will know that other life exists in the universe. Assuming
we know more Mersenne primes than they do, they will have stumbled onto new
"free" primes, at no computational cost. (Verification is easy, if they have a
Lucas-Lehmer test and can wait long enough, even with slow computers.) If
they're anything like us, one of them will raise the question if WE have heard
other civilizations with 37 Mersenne primes and simply repeated the primes out
ourselves. That would be a method of faking it. They can, however,
definitively put an UPPER limit on our technological achievement. If the other
society knows more Mersenne primes than we do, then they may or may not
realize the way of "faking" it, while if they know less Mersenne primes,
they'll probably realize my point.
<<Nope, they will just wonder what they have overlooked that makes Mersenne
Primes so basic to a culture.>>
Imagine if some exoculture sees our Mersenne prime message, and they feel that
THEIR culture is inferior because they only know the first four. And, there is
always Myxlptlk's Theorem to consider.
<<Except that it might have an unintended effect. Suppose we send out a list
of Mersenne primes, and the receiving civilization realizes from the list
that we do not know the Theorem of Myxlptlk, which, as every young
Golurdian knows, gives an explicit formula for all Mersenne primes.>>
What about the following scenario:
We send the Mersenne prime message. The friendly Aeraibvca civilization
receives it, and notices that we know far fewer Mersenne primes than they do.
Of course, they have existed for much longer, and have known about Mersenne
primes for hundreds of millennia. Thus, they're surprised that we have found
37 in just a couple of millenia, and most in the last century. We advance at a
much faster rate than them. They don't know Myxlptlk's Theorem (from the
Golurdians), but they do know a few more interesting facts about Mersenne
primes. They even learn a couple of things from us (General Relativity is
unknown to them - they only have Ntromdukian gravity), so they send us
everything they know about Mersenne primes, and even send us all the primes
that they know. Our comparatively primitive Terran mathematicians looks at the
new facts, conjectures, and all the new primes, and see some sort of a
pattern. Hrm. Separately, the Aeraibvcas and the Terrans couldn't have thought
of Myxlptlk's Theorem, but together, they derive an even-easier-to-compute-
with version of it (ha ha, Golurdians). Interesting.
On further thought, if we're willing to wait long enough, it could be a sort
of interstellar game we could play, even if we can't physically get there in a
reasonable amount of time.
Send the first 10 Mersenne primes to an alien civilization, including enough
(hahaha) information for them to deduce our language, or a special LinguaCode
specifically designed to be easy for alien civilizations to understand (why
make them deal with declensions and conjugations if they don't have to? Here's
what a few sentences might look like:
Ted picked up a book yesterday, and he quickly read it. Ted thought that the
book was very informative.
Ted before-pick book before-day. Ted fast before-read book. Ted before-think
book before-is very informative.
Or something like that.)
Then ask them how many Mersenne primes they know. Then send them a couple, and
they can send us a couple, so forth. It could be a race. Can we find the 137th
Mersenne prime before the Aeraibvcas do? Our superiority as a race is at
stake!
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From: Spike Jones <[EMAIL PROTECTED]>
Date: Sun, 28 Feb 1999 16:38:02 -0800
Subject: Mersenne: Spike - demonstrating calculating prowess
> George Strohschein wrote:Even a typical insect brain has many times the
> computing power of our best PCs.
Perhaps, but the bugs are using their brains for such mundane things,
such as building anthills and buzzing manure, whereas our PCs are
calculating and accumulating knowledge. Besides, our PCs are getting
better every year, whereas modern bugs are no smarter than their
amber-encased distant ancestors.
> Consider that it takes one PC to run a robot arm at Chrysler; a fly
> has six much more complicated legs.
But the Chrysler arm is making something useful to humans and our
idle PCs are too. Nowthen, someone mentioned the SETI suggestion
of sending out a list of the first 100 primes as a proof of intelligent
origen. Would it not be a far more impressive display to send out
the first 37 Mersennes? The first hundred primes were known back
who knows how long ago. Yawn. Ah, but a list of the first 37 Mersennes
demonstrates that we, as a species, are advanced and are to be treated
with respect, even by more advanced exosocieties.
Secondly, how many human endevours really include the entire human
species? GIMPS cares not your color, age, race, gender, where you
live or who/what you pray to. Mathematics transcends the boundaries
that we have built that divide us.
This characteristic leads me to extend a previous argument about using
primes to communicate with exos: is there any better way to break the
interstellar ice than to send out a list of primes? I have pondered this
for years, and have thought of none, except a related concept: sending
out a list of Mersenne primes.
Now George, if we could only teach flies to do Lucas Lehmer tests in
their idle moments.... {8^D spike
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From: George Woltman <[EMAIL PROTECTED]>
Date: Sun, 28 Feb 1999 14:01:21 -0500
Subject: Mersenne: Double-checking (was Chronons)
Hi,
At 07:35 PM 2/26/99 -0800, Spike Jones wrote:
>How about sweetening the pot for anyone who is doing double checking
>that discovers a mistake in the first LL analysis? How does this work?
>The first LL test returns a residual, then the double checking
>routine takes that residual and... what? How often is a result
>overturned by double checking?
>From your point of view a double-check is just like a first time test.
You run a Lucas-Lehmer test and when done send in your 64-bit residue.
I compare that residue to the first run and if they match, the exponent
is declared double-checked. If they don't match, a third test is run
to properly double-check the number.
Finding an error in the first LL test is not rare. I've said about 1 in
200 are incorrect. When the entire 1,400,000 - 2,000,000 range has
been double-checked I'll perform some more rigorous analysis of the
reliability of first-time LL results.
Best regards,
George
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From: Spike Jones <[EMAIL PROTECTED]>
Date: Sun, 28 Feb 1999 17:09:21 -0800
Subject: Re: Mersenne: Some diagrams
> Wojciech Florek wrote: If you are intersting in these plots browse to my
> page
> http://main.amu.edu.pl/~florek
> You can download pictures in *.gif *.ps and *.tex format.
Wow thanks Wojciek! Great web site.
I know that we have many active GIMPSers all over the U.S., Australia
and Europe. Are there GIMPSers from China? From Africa? I surely
hope so, for GIMPS is a rare example of an entire planet working
together on a project. spike
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From: "Aaron Blosser" <[EMAIL PROTECTED]>
Date: Sun, 28 Feb 1999 19:21:51 -0700
Subject: RE: Mersenne: Fabs.
> [mailto:[EMAIL PROTECTED]]On Behalf Of Terry S. Arnold
> Aaron
>
> You got the resistance part wrong. As the trace gets smaller the
> resistance
> increases because the cross-section of the trace gets smaller.
Doh! Of course you're right. There is a benefit though in having the
traces use shorter runs, even though their width decreases.
FWIW, Intel keeps the resistance of a cross-section *about* the same when
they reduce the width, by making it, erm..."taller" when possible. But I
suspect much of the clock speed increases come from lower voltages also.
Also FWIW, the package of a PII is nothing more than the CPU and a couple of
chips for the L2 cache. It's *possible* that the first Celerons were PII's
with failed L2 cache chips that were then disabled, but not likely. Since
they are seperate chips and are assembled in the package, each chip is
tested prior to packaging and there wouldn't really be any PII's with bad
cache.
If you opened a PII or Celeron cartridge, you'd see that the Celeron
(cacheless) is just plain missing those extra 2 chips. It's not really like
the 486sx which were 486DX chips with the FPU purposely disabled.
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From: Bryan Fullerton <[EMAIL PROTECTED]>
Date: Sun, 28 Feb 1999 23:45:07 -0500
Subject: Re: Mersenne: Fabs.
On Sun, Feb 28, 1999 at 07:21:51PM -0700, Aaron Blosser <[EMAIL PROTECTED]> wrote:
>
> Also FWIW, the package of a PII is nothing more than the CPU and a couple of
> chips for the L2 cache. It's *possible* that the first Celerons were PII's
> with failed L2 cache chips that were then disabled, but not likely. Since
> they are seperate chips and are assembled in the package, each chip is
> tested prior to packaging and there wouldn't really be any PII's with bad
> cache.
I suspect the problem was with the cache controller on the CPU, much like...
> the 486sx which were 486DX chips with the FPU purposely disabled.
... which were disabled because they failed QA testing.
Bryan
- --
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Owner, Lead Consultant http://www.feh.net/
Samurai Consulting http://www.icomm.ca/
"No, we don't do seppuku." Can you feel the Ohmu call?
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From: Spike Jones <[EMAIL PROTECTED]>
Date: Sun, 28 Feb 1999 23:17:35 -0800
Subject: Mersenne: mersennes for exocivilizations
[EMAIL PROTECTED] wrote:
> Then ask them how many Mersenne primes they know. Then send them a
couple, and
> they can send us a couple, so forth. It could be a race. Can we find
the 137th
> Mersenne prime before the Aeraibvcas do? Our superiority as a race is
at stake!
Let me turn this around. When or if we ever receive signals from
exocivilizations, those signals might well be in the form of a list of
primes, as in Sagan's excellent book and now movie Contact.
It would not surprise me at all if instead of a list of primes, they
send us the series 2,3,5,7,13,19,31,61,89,107,127,521...
If they did, most scientists would be baffled, but you and I would get
it. We
would grok that message bigtime. We would be among the approximately
50,000 humans of 6E9 that would grok that message immediately without
having to look it up. spike
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From: Luke Welsh <[EMAIL PROTECTED]>
Date: Mon, 01 Mar 1999 00:07:38 -0800
Subject: Re: Mersenne: mersennes for exocivilizations
At 11:17 PM 2/28/99 -0800, Spike Jones wrote:
>It would not surprise me at all if instead of a list of primes, they
>send us the series 2,3,5,7,13,19,31,61,89,107,127,521...
or 2, 3, 5, 7, 13, 17, 19, 31, 67, 127, 257 perhaps?
- --Luke
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From: Todd Sauke <[EMAIL PROTECTED]>
Date: Mon, 1 Mar 1999 12:03:17 -0800
Subject: Re: Mersenne: Re: Mersennes for Martians
Spike Jones wrote:
>
>Can anyone think of any way to *prove* the level of sophistication
>of our current society, better than a list of Mersenne primes? spike
You can never *prove* your level of sophistication to a less sophisticated
society with a mere list of Mersenne primes. They would have no way to
know if it was correct. When this discussion started, I think the point
was how impressive Lucas Lehmer testing is compared to brute force
factoring. Without LL (or equivalent) AND the computational ability to
carry it out exhaustively for all candidates up to the largest member of
the list, they wouldn't be able to verify the list and would have to take
it on faith. (They might well be impressed if they chose to believe the
claim, but it won't have been *proven*.) In order to *prove*
sophistication to a non LL society, we would have to teach them the Lucas
Lehmer theorum, unfortunately a lot trickier than sending a list of numbers.
Todd Sauke
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From: David L Nicol <[EMAIL PROTECTED]>
Date: Mon, 01 Mar 1999 16:32:44 -0600
Subject: Re: Mersenne: Fabs.
Aaron Blosser wrote:
> IBM uses copper in some of it's ASIC (application specific integrated
> circuit) using .16 micron technology. Those bad boys are fast...up to
> 800MHz. And I think IBM fabs some PowerPC's using copper, but curiously
> those are running around 400MHz.
>
> Intel says they can keep using aluminum up to about .13 micron width at
> which time aluminum just don't get much smaller. So then they'll go to
> copper, and I can gaurantee they're already doing research with copper,
> thanks to what an anonymous Intel folk shared with me recently.
http://www.microprocessor.sscc.ru/news/
Yikes! Apparently the "Elbrus E2K" is a 0.18 micron *386 compatible
running at 1.2GHz
All the Digital/Compaq Alpha chips use .35 micron fabs.
________________________________________________________________________
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++++ stop the execution of Mumia Abu-Jamal ++++
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From: [EMAIL PROTECTED]
Date: Mon, 1 Mar 1999 16:55:40 EST
Subject: Mersenne: Re: Spike - demonstrating calculating prowess
> Would it not be a far more impressive display to send out
> the first 37 Mersennes?
Yes... and it would be even more impressive to display the first 40 Mersenne
Primes.
- -Phil Busby
http://members.aol.com/ltjglotus/
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From: "=?iso-8859-1?Q?Ignacio_Larrosa_Ca=F1estro?=" <[EMAIL PROTECTED]>
Date: Tue, 2 Mar 1999 00:56:36 +0100
Subject: Mersenne: RV: billions, trillions, ...
> 1E15 is a quadrillion dammit! 1E12 is a trillion!!! <g>
ĦUhmm..! In Europe usually a billion is 1E12 and a trillion is 1E18.
1E15 is thousand billions...
Ignacio Larrosa
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From: Andrew Isaacson <[EMAIL PROTECTED]>
Date: Mon, 1 Mar 1999 19:18:57 -0500
Subject: Re: Mersenne: Fabs.
On Mon, Mar 01, 1999 at 04:32:44PM -0600, David L Nicol wrote:
> http://www.microprocessor.sscc.ru/news/
> Yikes! Apparently the "Elbrus E2K" is a 0.18 micron *386 compatible
> running at 1.2GHz
The E2K is not in production; it's just a design on paper (well, on
disk I suppose) right now, and unless they get some outside funding
the designers will not be able to take it beyond that state. Granted,
it's a very compelling design, and there's no reason to think they
wouldn't be able to make it given the resources, but one thing they
don't say is how much it would cost...
> All the Digital/Compaq Alpha chips use .35 micron fabs.
The modern ones do, anyways. The older Alphas used .5 micron (or
larger?), and there are Alphas on the drawing boards that will target
a smaller process.
What does this have to do with Mersenne primes again?
- -andy
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From: Luke Welsh <[EMAIL PROTECTED]>
Date: Mon, 01 Mar 1999 17:57:34 -0800
Subject: Mersenne: Mathematica's Parallel Computing Toolkit
Beta
"...parallel programming over a network of heterogeneous machines..."
http://www.wolfram.com/news/parallel.html
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From: "Aaron Blosser" <[EMAIL PROTECTED]>
Date: Mon, 1 Mar 1999 20:05:18 -0700
Subject: RE: Mersenne: Fabs.
> On Mon, Mar 01, 1999 at 04:32:44PM -0600, David L Nicol wrote:
> > http://www.microprocessor.sscc.ru/news/
> > Yikes! Apparently the "Elbrus E2K" is a 0.18 micron *386 compatible
> > running at 1.2GHz
>
> The E2K is not in production; it's just a design on paper (well, on
> disk I suppose) right now, and unless they get some outside funding
> the designers will not be able to take it beyond that state. Granted,
> it's a very compelling design, and there's no reason to think they
> wouldn't be able to make it given the resources, but one thing they
> don't say is how much it would cost...
Hmmm...it looked at least like they had some prototypes...oh well.
Vaporware...
> What does this have to do with Mersenne primes again?
Finding 'em faster! :-) Discussing ways to optimize the speed of the
programs by using some of the nifty new instructions/capabilities of the new
processors coming out (like the PIII, AMD K6-3, Merced, etc).
Aaron
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From: Spike Jones <[EMAIL PROTECTED]>
Date: Mon, 01 Mar 1999 21:57:59 -0800
Subject: Mersenne: who has the most wicked-fast home setup?
Let category 1 GIMPSers be set that contains those GIMPSers that
use a number of commercially owned or institutional computers, such
as the champion TempleU.
Let category 2 GIMPSers be set that contains those GIMPSers that
use a combination of commercial and home computers.
Let category 3 GIMPSers be set that contains those GIMPSers that
use only computers located in the home of that GIMPSer and owned
by that GIMPSer.
Are there any cat 3 GIMPSers in the top 100 producers? Top 200?
Who is the highest ranking cat 3 GIMPSer?
I am a cat 3 and last I checked I was 1500 something. spike
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From: Spike Jones <[EMAIL PROTECTED]>
Date: Mon, 01 Mar 1999 23:09:28 -0800
Subject: Re: Mersenne: mersennes for exocivilizations
So these were the exponents that old Mersenne *thought* were his
namesakes? spike
Luke Welsh wrote:
> At 10:01 PM 3/1/99 -0800, you wrote:
> >Im stumped. What is 2, 3, 5, 7, 13, 17, 19, 31, 67, 127, 257... ? spike
>
> Gotcha!
>
> http://www.scruznet.com/~luke/lit/lit_069s.htm
> http://www.scruznet.com/~luke/lit/lit_002.txt
> http://www.scruznet.com/~luke/lit/lit_019.htm
> http://www.scruznet.com/~luke/biblio.htm
>
> --Luke ;-)
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End of Mersenne Digest V1 #517
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