Mersenne Digest Saturday, 13 March 1999 Volume 01 : Number 529
----------------------------------------------------------------------
From: "Brian J Beesley" <[EMAIL PROTECTED]>
Date: Thu, 11 Mar 1999 09:34:13 GMT
Subject: Re: Mersenne: AMD CPU
"George Strohschein" <[EMAIL PROTECTED]> writes:
> My new AMD CPU reported a sum check error while double
checking. I suppose
> you would change to Intel while it's still possible?
User with K6/2 processors 350 MHz and faster, be aware that you
need to apply a patch (available from Microsoft site) if you are
running Win 9x to correct a problem in the Windows kernel
triggered by these processors.
Regards
Brian Beesley
________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
------------------------------
From: [EMAIL PROTECTED]
Date: Thu, 11 Mar 1999 09:37:27 EST
Subject: Mersenne: Banach-Tarski
In the early 1920's, two guys named Banach and Tarski were exploring a
rather obscure branch of mathematics, later called by physicists and
mathematicians, "a
somewhat surreal corner of set theory". They came up with some theorems known
as the
Banach-Tarski theorems (BTT). Now remember, these were not speculations but
theorems which they could prove. Here is just one example of what comes out
of BTT:
start with a solid sphere, like a bowling ball with no finger holes. This one
sphere can be
cut into five pieces so that two of them can be reassembled into another solid
sphere
identical to the original; the remaining three pieces (guess what's coming)
can also be
reassembled into another solid sphere identical to the original. And so on.
Surreal indeed!
But people just viewed it as an oddity with no application to the real world
until...
After QCD was thoroughly tested and accepted by most physicists, a fellow
named
Augenstein, who knew about BTT and QCD, looked at the math involved in both
and
showed that the rules governing sets and subsets in BTT were formally exactly
the same
as the rules that described the behaviour of quarks and other entities in QCD.
One
example of something that happens in the real world of physics is this: when a
single
proton is accelerated and smashed into a metal target, it can produce many new
copies of
itself. This is exactly like the proliferation of bowling balls described by
BTT! Thus again
pure math became applied math decades later.
________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
------------------------------
From: Greg Hewgill <[EMAIL PROTECTED]>
Date: Thu, 11 Mar 1999 07:42:14 -0800
Subject: Re: Mersenne: Mersenne Machine & Single Floppy LL Tester
On Thu, Mar 11, 1999 at 10:05:06AM +0000, Brian J Beesley wrote:
> (1) I don't see why you can't eliminate the networked P90 by
> adding hard disk etc. to one of the other systems & using that as
> an NFS server / HTTP proxy.
I already had the P90 installed with all the necessary networking support
(two network cards, HTTP proxy, and so on). It was already there, why not
use it? Besides, it's doing factoring. :)
> (2) 32MB DRAM is a bit stingy - as FFT size grows, so does the
> memory requirement - and it's a bit silly to run with swap space on
> a remote-mounted disk. I'd spend a few dollars extra & go for 64MB
> DRAM.
Here's the memory usage line from 'top' on one of the machines:
Mem: 31184K av, 7848K used, 23336K free, 4032K shrd, 4K buff
Swap: 0K av, 0K used, 0K free 1796K cached
With 23 MB of 32 MB free, I don't think I'm going to run into memory
constraints anytime soon.
> 3) Some motherboards complain bitterly if they find no graphics
> adapter at boot time. Either you don't have this problem, or you
> have real cheap VGA adapters fitted.
I have one cheap VGA adapter that I used to set up the machines. The
motherboard I'm using (ABIT BH6) doesn't complain if there is no video.
It beeps a couple of times on startup, but otherwise has no problem with it.
Greg Hewgill
________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
------------------------------
From: Jud McCranie <[EMAIL PROTECTED]>
Date: Thu, 11 Mar 1999 10:15:10 -0500
Subject: Re: Mersenne: M(M3021377)
At 11:52 PM 3/10/99 -0800, John R Pierce wrote:
>> How long would it take to run LL testing on M(M3021377) asuming that this
>> number was prime. Could we complete it before the sun explodes?
>
>Oh, I suspect if we could build a computer with a bunch of 4 million bit wide
>multipliers that ran at a few terahertz it would take significantly less time
>than that.
The number of steps for the L-L test would bee too large my many, many
orders of magnitude.
+------------------------------------------+
| Jud McCranie [EMAIL PROTECTED] |
+------------------------------------------+
________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
------------------------------
From: "Nicolau C. Saldanha" <[EMAIL PROTECTED]>
Date: Thu, 11 Mar 1999 15:43:48 -0300 (EST)
Subject: Mersenne: M(M127) andB M(M3021377)
On Wed, 10 Mar 1999, John R Pierce wrote:
> > All,
> > How long would it take to run LL testing on M(M3021377) asuming that this
> > number was prime. Could we complete it before the sun explodes?
>
> Oh, I suspect if we could build a computer with a bunch of 4 million bit wide
> multipliers that ran at a few terahertz it would take significantly less time
> than that.
I think the first big problem is not time, but space. If you want to perform LL
on Mp you have to keep track of numbers modulo Mp, which requires aprox. p
bits. So even if you allow for one terabyte of memory/temporary files,
p must be at most aprox. 8 * 10^12. I forget how many bits of memory
the lithiumverse was supposed to have, but I am sure it was much much less
than M3021377. The number of iterations would also be aprox. M3021377,
so even if you perform 10^34 iterations per second you don't have enough
time...
Some mathematician asked (conjectured?) whether M(M(M(M(...(2)...)))
is always prime; the first unknown case is M(M127),
and that already requires (for LL) around M127 ~= 10^38 bits of memory and
iterations, which is far beyond present technology
(but easy for the lithimverse).
________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
------------------------------
From: Jud McCranie <[EMAIL PROTECTED]>
Date: Thu, 11 Mar 1999 15:52:43 -0500
Subject: Re: Mersenne: Banach-Tarski
At 09:37 AM 3/11/99 -0500, [EMAIL PROTECTED] wrote:
>In the early 1920's, two guys named Banach and Tarski were exploring a
This is getting off-topic, but the B-T theorem requires you to accept the
axiom of choice (which most mathematicians do). Here's some info:
http://www.cs.unb.ca/~alopez-o/math-faq/node70.html
________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
------------------------------
From: Jud McCranie <[EMAIL PROTECTED]>
Date: Thu, 11 Mar 1999 19:29:27 -0500
Subject: Re: Mersenne: M(M127) andB M(M3021377)
At 03:43 PM 3/11/99 -0300, Nicolau C. Saldanha wrote:
>Some mathematician asked (conjectured?) whether M(M(M(M(...(2)...)))
>is always prime; the first unknown case is M(M127),
Another version of the conjecture is that M(M(p)) is prime where M(p) is a
Mersenne prime. I think that the first one that fails to be prime is
M(8191) = M(M(13)).
+--------------------------------------------------------+
| Jud McCranie [EMAIL PROTECTED] |
| |
| 127*2^96744+1 is prime! (29,125 digits, Oct 20, 1998) |
+--------------------------------------------------------+
________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
------------------------------
From: Joth Tupper <[EMAIL PROTECTED]>
Date: Thu, 11 Mar 1999 20:17:29 -0500
Subject: Mersenne: Banach-Tarski
Message text written by INTERNET:[EMAIL PROTECTED]
>Banach-Tarski theorems (BTT).<
Hey, thanks for straightening out my misrecollection.
Joth
________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
------------------------------
From: "Terry S. Arnold" <[EMAIL PROTECTED]>
Date: Thu, 11 Mar 1999 20:10:59 -0800
Subject: Mersenne: Mersenne Cryptosystem
If I remember right there was mention a while back of a cryptographic
algorithm based on Mersenne primes. Can anyone give a pointer to
information on this cryptographic algorithm?
Terry
Terry S. Arnold 2975 B Street San Diego, CA 92102 USA
[EMAIL PROTECTED] (619) 235-8181 (voice) (619) 235-0016 (fax)
________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
------------------------------
From: Conrad Curry <[EMAIL PROTECTED]>
Date: Thu, 11 Mar 1999 22:33:10 -0600 (EST)
Subject: Re: Mersenne: M(M127) andB M(M3021377)
> At 03:43 PM 3/11/99 -0300, Nicolau C. Saldanha wrote:
>
> >Some mathematician asked (conjectured?) whether M(M(M(M(...(2)...)))
> >is always prime; the first unknown case is M(M127),
>
> Another version of the conjecture is that M(M(p)) is prime where M(p) is a
> Mersenne prime. I think that the first one that fails to be prime is
> M(8191) = M(M(13)).
I.J. Good discusses this conjecture in his paper "Conjectures
Concerning Mersenne Numbers," MTAC(Math. Comp.), v.9, pp. 120-121, 1955.
He suggests the probability of M(M127) being prime is negligible.
Also see Robinson's paper in Luke's bibliography
http://www.scruznet.com/~luke/lit/lit_024s.htm
Will Edgington maintains a status of these numbers at
http://www.garlic.com/~wedgingt/MMPstats.txt
Links to programs that can factor these numbers can be found on
the Mersenne freeware page at
http://www2.netdoor.com/~acurry/mersenne/freeware.html
________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
------------------------------
From: "Vincent J. Mooney Jr." <[EMAIL PROTECTED]>
Date: Fri, 12 Mar 1999 02:58:54 -0500 (EST)
Subject: Re: Mersenne: Mersenne Cryptosystem
Try this:
Nelson H. F. Beebe <[EMAIL PROTECTED]>
Center for Scientific Computing
University of Utah
Department of Mathematics, 322 INSCC
155 S 1400 E RM 233
Salt Lake City, UT 84112-0090
USA
Publication began with volume 1, number 1, in January 1977, when I began
my subscription, and the journal currently appears quarterly, in January,
April, July, and October. Volume 9, number 3, appeared in June, instead of
July, 1985. My subscription lapsed some years ago. Originally it was
published and/or edited at Rose-Hulman Institute of Technology, Terre Haute,
IN 47803, USA, and then moved in July 1995 to the Department of Mathematical
Sciences, United States Military Academy, West Point NY 10996-9902, USA.
Cryptologia is a laymen's publication, in the main, but has some heavy
math. Mr. David Kahn, author of CODEBREAKERS (an excellent book just from
the point of history), writes for it and other notable persons in the field
did also. This journal is unusual in that volumes are numbered with roman,
rather than arabic, numbers. For convenience of bibliography tools like
bibsort, this bibliography uses the equivalent arabic form. If Mersenne
primes have been used in cryptology, these people will know. See the web
site http://liinwww.ira.uka.de/bibliography/Misc/cryptologia.html for some
info and the journal has a World-Wide Web site at
http://www.dean.usma.edu/math/resource/pubs/cryptolo/index.htm
At 08:10 PM 3/11/99 -0800, Terry wrote:
>If I remember right there was mention a while back of a cryptographic
>algorithm based on Mersenne primes. Can anyone give a pointer to
>information on this cryptographic algorithm?
>
>Terry
>Terry S. Arnold 2975 B Street San Diego, CA 92102 USA
>[EMAIL PROTECTED] (619) 235-8181 (voice) (619) 235-0016 (fax)
>________________________________________________________________
>Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
>
________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
------------------------------
From: Jud McCranie <[EMAIL PROTECTED]>
Date: Fri, 12 Mar 1999 08:50:40 -0500
Subject: Re: Mersenne: M(M127) andB M(M3021377)
At 03:43 PM 3/11/99 -0300, Nicolau C. Saldanha wrote:
>I think the first big problem is not time, but space.
No, time will be the limiting factor for testing M(n). I have 320
megabytes, so if you devote 300 megs to data, I have enough space to test
M(1,200,000,000). I certainly don't have enough time to test that. The
space required is a linear function of n whereas the time required is at
least a quadratic function of n, so the time requirement grows much more
rapidly than the space requirement.
+-------------------------------------------------+
| Jud McCranie [EMAIL PROTECTED] |
| |
| You'll never need more than 640 megs of memory. |
+-------------------------------------------------+
________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
------------------------------
From: "Mauricio J. A. Latorre A." <[EMAIL PROTECTED]>
Date: Fri, 12 Feb 1999 17:02:50 +0400
Subject: Mersenne: Supercomputer
I have 4 celeron 300A, and i want to make-it an array.
How i can found information?
Mauricio -=\Chubasco/=- Latorre
________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
------------------------------
From: The thrill of minimalism <[EMAIL PROTECTED]>
Date: Fri, 12 Mar 1999 22:35:53 +0000
Subject: Mersenne: free sphere is half deflated
"Ernst W. Mayer" wrote:
>
> Joth Tupper writes:
>
> >the Bolzano-Tarski theorem proved (what, back in the 1920's?)
> >that you could cut a solid 3D sphere into finitely many chunks,
> >then rearrange the chunks to make another solid (no holes or gaps)
> >3D sphere with _twice_ the volume. Pretty spooky, I always felt.
>
> I don't know about spooky, but 'twould seem to violate conservation
> of mass (or mass/energy, if you're a postmodern relativist :),
> 'twouldn't it?
You can map a line segment of "length" 1 onto two line segments of
length 1 with a simple mapping function f(x)=2x+1 for instance.
This maps all the points from 0 to 0.5 onto the line segment from
1 to 2 and the points from 0.5 to 1 onto 2 to 3.
One "chunk."
a "two chunk" mapping of the same points might look like this:
f(x)={
x < 0.25 && return 3+4x
x >= 0.25 && return 4+4x/3
}
They're dealing with geometric volume, not fluid volume.
________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
------------------------------
From: Joth Tupper <[EMAIL PROTECTED]>
Date: Fri, 12 Mar 1999 17:47:20 -0500
Subject: Mersenne: Bolzano-Tarski-Milstein-Nicol
>>Message text written by The thrill of minimalism
>>>
>>Joth Tupper wrote:
>>> the Bolzano-Tarski
>>> theorem proved (what, back in the 1920's?) that you could cut a solid
3D
>>> sphere into finitely many chunks, then rearrange
>>> the chunks to make another solid (no holes or gaps) 3D sphere with
_twice_
>>> the volume. Pretty spooky, I always felt.
>>> Robinson first proved that 9 chunks would do it. Then he found a way
with
>>> 5 (maybe it is 4) and I think he showed that this
>>> was the minimum.
>>Thanks so much to whoever posted the link to the reference on the
>>choice axiom, which allows the BTT result.
>>All the talk of "cutting
>>and rearranging" can be so misleading as it makes it sound as
>>if the BTT is a magic trick you can do to a common household orange
>>with a common household steak knife, which simply is not the case.
>>The mathematical results deal with mapping sets. For instance in
>>the BTT the fifth "piece" is the single center point of the sphere,
>>which isn't much of a "chunk" in any real sense.
>>Equivalenting 1-1 mapping and "volume" is confusing. "Volume" must
>>have become technical math jargon at some point.
>>When you set up a mapping of a line segments to two other line
>>segments of the same length, such as f(x)=2x, you call that length
>>length, and calling the points in the BTT spheres "volume" is
>>an extension of that metaphor.
>>the "chunks" in question is about what is the simplest way to
>>arrange the mapping, it's not a wooden puzzle.
>>Still spooky? Or am I just being a raving idiot.
<
Volume is a technical term in every setting. In 3D analysis, volume starts
out as the
simple idea that a cube of side 1 contains 1 unit of volume. Trouble is
that 3D has enough room
to work that non-measurable sets pop up in many contexts, such as BTT.
Non-measurable sets in
1D are tricky to construct but do exist.
As I understand it, the sphere doubling notion is not as trivial as using
f(x) = 2x to map [0,1] to [0,2].
You "cut" (with a "knife" that can separate points) the sphere into
finitely many pieces, and using translations
and rotations only (i.e., length preserving motions) reassemble the
finitely many pieces into a bigger whole with
no holes. R.Robinson was not a trivial mathematician and this is one of
his better known results.
________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
------------------------------
From: Spike Jones <[EMAIL PROTECTED]>
Date: Mon, 08 Mar 1999 20:44:32 -0800
Subject: Re: Mersenne: *P*M3021377 in base 62
David L Nicol wrote:
> > Have we any code gurus that can help us out here? spike
>
> I'm not going to do this one. Spike, if you search for base-64
> encoding libraries you'll find several you can slightly mutate to
> get what you want, similar to base64 (MIME) encoding as it is...
I thought of using one of the canned routines but any base that
is a factor of only 2 will give you the same uninteresting result:
a bunch of [symbol for 63] followed by a bunch of 0s.
I ashamed to admit my coding skills have so atrophied that I
am probably unable to modify a base64 to a base62. {8-[ spike
________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
------------------------------
From: Spike Jones <[EMAIL PROTECTED]>
Date: Mon, 08 Mar 1999 20:44:04 -0800
Subject: Mersenne: Re: Who wants M37 and it's Perfect number?
Ashton Vaz wrote:
> I think someone wanted M37 and it's associated perfect number. I
> have both numbers sitting in text files on my computer...Was it you
> Spike?
Yes it was! This notion of converting the digits to colors is a
cool one. What other ideas can we derive? We have discussed
changing bases, but our fun comes to an end with the next Mersenne
prime to be discovered, as it will have at least twice as many
digits, probably more like three times as many and will likely
be discovered in 1999 or 2000.
We could use all the printable ASCII characters minus the ones
already spoken for: =,+,-,/,*,(,),<,>, etc, then make it into
a base hundred and something, thus half as many digits as would
be needed in base 10. I want to keep it to about 6 pages.
Do email me the numbers if it is convenient Ashton. {8-]
thanks! [EMAIL PROTECTED] microsloth word or text file is fine.
________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
------------------------------
From: "Aaron Blosser" <[EMAIL PROTECTED]>
Date: Fri, 12 Mar 1999 22:56:43 -0700
Subject: Mersenne: Prime95 errors with RPCNET.DLL
Hello all,
I was just setting up another slew of machines, 12 right now with maybe 20
to follow right away and maybe 30 more after that, (don't worry, I have
permission! :-) but I was running into a strange situation.
These machines are currently mine to tinker with, but I don't have network
connections for all of them at the moment. No problem, I can use the manual
testing page at entropia.com to get worktodo files, but in the meanwhile,
they're not network connected.
Here's the problem. They want to talk to the IPS...but without a network
connection, every time they try to connect, Prime95 crashes.
Hmmm...that's no good.
I fixed it by changing the communication method from RPC to HTTP...I suppose
that will work just fine, but since our firewall was passing RPC okay, I am
wondering if there are any long term benefits of one over the other.
And has anyone else noticed this bizarre behaviour? I seem to recall a
thread regarding this on the mailing list before, but I'm not sure.
So RPC vs HTTP and then RPC crashing with no network connection.
Thanks folks,
Aaron
________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
------------------------------
From: "Paul Missman" <[EMAIL PROTECTED]>
Date: Sat, 13 Mar 1999 10:15:04 -0500
Subject: Re: Mersenne: Prime95 errors with RPCNET.DLL
Yes, I had this problem. These problems are documented in the FAQ,
on Primenet, which I didn't read beforehand either. Perhaps HTTP
would be a better choice for the default value in the next release
of Prime95. If HTTP had been the default, I imagine most people
would never have experienced the problem.
Paul Missman
From: Aaron Blosser <[EMAIL PROTECTED]>
>
>Here's the problem. They want to talk to the IPS...but without a network
>connection, every time they try to connect, Prime95 crashes.
>
>And has anyone else noticed this bizarre behaviour? I seem to recall a
>thread regarding this on the mailing list before, but I'm not sure.
________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
------------------------------
End of Mersenne Digest V1 #529
******************************
