Mersenne Digest Monday, 8 March 1999 Volume 01 : Number 524
----------------------------------------------------------------------
From: Dennis Goudy <[EMAIL PROTECTED]>
Date: Sun, 7 Mar 1999 15:29:06 -0800 (PST)
Subject: Mersenne: Reminiscing
On the subject of prehistoric computers, my first home computer was a
Heathkit H8 with no monitor, I/O using audio cassettes, and it was
thrilling.
In 1958 I was programming an IBM 705 with a cycle time of 17 usec, and
it was unbelievably fast. I think only the government could afford one.
Amazing!
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From: Joth Tupper <[EMAIL PROTECTED]>
Date: Sun, 7 Mar 1999 18:54:08 -0500
Subject: Re: Mersenne: mersennes for exocivilizations
One problem that seems hidden in transmitting a large Mersenne numbers is
the difficulty in decoding a very long string
of binary 1's. Apart from a constant signal being non-random, how does a
receiver know when it starts and stops? And
how do they guess how to parse it.
I hate to paraphrase a comic, but compared to a Cobol core-dump, Joan
Rivers', "Can we talk?" is easily understood.
Sending Mersennes looks like a singularly difficult way to get somebody's
attention.
Joth Tupper
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From: "Clayton Smith" <[EMAIL PROTECTED]>
Date: Sun, 7 Mar 1999 18:46:35 -0500
Subject: Re: Mersenne: biiiiig perfect number
>I once had a great idea: I would express the Great Number in hex!
>Then I realized that I would get with 4 pages of tiny Fs. {8-[
>Not so interesting. But if some clever GIMPSer were to generate the
>perfect number that is (M37*(M37+1))/2 then express *that* number
>in hex, I would clear off a space on my office wall for it. {8-] Anyone
>accept the challenge?
I'm afraid the perfect number in hex would be equally boring... Let P =
2^p - 1, a Mersenne prime. The associated perfect number is:
P(P+1)/2 = (2^p - 1)(2^p)/2 = (2^p - 1)(2^(p-1))
The binary expansion of this number will of course be p 1's followed by p-1
0's. In hex it would be equally boring.
- - Clayton
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From: Spike Jones <[EMAIL PROTECTED]>
Date: Sun, 07 Mar 1999 17:04:02 -0800
Subject: Mersenne: *P*M3021377 in base 62
> spike wrote: ... if some clever GIMPSer were to generate the
> >perfect number that is (M37*(M37+1))/2 then express *that* number
> >in hex, I would clear off a space on my office wall for it. {8-]
Clayton Smith wrote:
> The binary expansion of this number will be p 1's followed by p-1
> 0's. In hex it would be equally boring.
Yes, of course, so it would. Many others pointed this out to me too.
Dont I feel silly. Thanks to all who replied to the flawed meme. {8^D
The problem with having a bunch of mathematicians for friends: ya cant
get away with logic errors. {8^D
So, let us devise a way to express the Perfect number corresponding with
M3021377 (does it have a name? Let me call it *P*M3023177) in some
large
enough base to keep *P*M3021377 to about 8 pages or less if printed in
2 point font. It would be impressive if we could devise a way to print
out
100 different symbols so that it we could have it in base 100.
Imagine pointing out to your coworkers: this is the 1s column, next to
it
the 100s, then the 10,000s column... Unfortunately, I dont think there
are that many printable ASCII characters, if one stays in a single font,
which disallows jumping back and forth between Geneva and Greek
characters, for instance.
On second thought, maybe it is good to use base 62, with 0-9 doing the
usual task, A-Z representing 10-35 and a-z representing 36-61. It would
require only about 12% more symbols to express *P*M3021377
in base 62 as it would to express M3021377 in base 10, so it
would take about 7 pages in 2 point.
Then yahoos could search for their name in *P*M3021377, and such as
that, and attach cosmic significance to their finds, etc. {8^D
Have we any code gurus that can help us out here? spike
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From: "Clayton Smith" <[EMAIL PROTECTED]>
Date: Sun, 7 Mar 1999 21:11:43 -0500
Subject: Re: Mersenne: Moo?
>Yes, it would take an enormous amount of RAM to do this, but what if we
>stored the data in some kind of compressed format (a ZILLION to 1
>compression???), or some kind of reference format? Then we could take
>advantage of everyone's clock cycles used on other searches. There's got
>to be a way of virtually referencing somthing that is not able to exist.
>Look at the way we use a MOD instead of the actual number.
>
>Just some ramblings...
If we compressed the data by any constant factor (e.g. a zillion), the
amount of data to be stored would still double with each squaring, so we'd
be not much better off.
Suppose we had sufficient memory available to do the computation. How long
would it take? Assume we've discovered something better than FFT and can
multiply in O(n) time (as far as I know, this is the best that can be done
since you have to at least look at the whole number). Each S(n) is twice
the length of the previous one, and the squarings would take O(2^n) time. 1
+ 2 + 2^2 + ... 2^(n-1) = 2^n, so the whole computation would take O(2^n)
time. That's a lot of time! And of course, actually dividing M(n) into
S(n-2) would take just about as long.
- - Clayton
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From: schaz <[EMAIL PROTECTED]>
Date: Sun, 7 Mar 1999 20:18:52 -0800
Subject: Mersenne: Re: Mersenne Digest V1 #523
Chuck
Since the LL algorithm is:
L[1] = 4
for i = 1 to P-2
L[i] = mod((L[i-1]^2 -2),((2^P)-1))
next i
I would want a very fast arbitrarily long squarer, and a very
fast arbitrarily long mod operation. Generating the (2^P)-1 is
fast and easy anyway.
So I guess that the instruction set would have to add ALS
(Arbitrarily Long Square) and ALM (Arbitrarily Long Mod) to
whatever else was needed to make the machine run.
Sunday, Sunday, March 07, 1999, you wrote:
mdirabc> Mersenne Digest Sunday, 7 March 1999 Volume 01 : Number 523
mdirabc> From: [EMAIL PROTECTED]
mdirabc> Date: Sun, 7 Mar 1999 11:43:59 -0800 (PST)
mdirabc> Subject: Mersenne: Mersenne Processor
mdirabc> If one were to build a microprocessor SPECIFICALLY suited to LL testing,
mdirabc> what would the assembly instruction set look like? Approximately what
mdirabc> would the architecture look like? Speed shouldn't be an issue because
mdirabc> there's never enough anyway and we're trying to work smarter not harder.
mdirabc> Thanks,
mdirabc> - -Chuck
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From: "Aaron Blosser" <[EMAIL PROTECTED]>
Date: Mon, 8 Mar 1999 11:27:25 -0700
Subject: RE: Mersenne: Category 1,2 or 3 ?
> My boss knows what is going on, but we were bought out before xmas by
> Nokia, I believe they have a policy of 'approved' software only.
> Nobody has
> got round to checking our site yet, but I am putting together a case to
> keep running the software. Best reference I have so far is Marc Getty and
> TempleU <G>
Good luck with that then... As for me, my current boss is sympathetic to
my strange desire to find prime numbers and is actually digging up about 70
machines and a couple midrange *NIX boxes just for me to goof around
with... He's ever so much cooler than US WEST! :-)
I showed him the TempleU team's page, and some other team pages where
they're using lots of computers with no ill effects, plus I've been running
it on some non-production machines lying around. He thinks it's pretty
cool stuff. Now I just need to convince him to run it on his machine! :-)
> Yep, they would be miles clear at the top by now. BTW I think that their
> actions were way over the top and as for calling in the FBI....I
> just hope
> that when it is all resolved that common sense and sanity
> prevails and that
> you get back your good name and all your equipment.
Thanks...I'm still waiting and wondering what will come of all this. Had I
known they would have reacted as they did, I wouldn't have used my own
account, maybe just used the challenge account or something. They still
would have known it was me, since I really didn't try to hide it at all,
but it's not like I just wanted to shoot to the top of the list. I was
already doing pretty good. At the time, I already had over 10 CPU years to
my name which put me in the top 50 I think, and at points in the past I was
in the top 10...all of that without the US WEST machines.
> >I *used* to have as many as 5 computers at my home running, but with my
> >current situation I'm lucky to have one P166 and a laptop on loan from
> >work...double sigh...
>
> Well you never know, when I found M2976221 it was on my only home pc, the
> P100. Mind you now that exponents are getting larger...I am
> current testing
> in the 20million range on the PII-300. It started last July and will be
> finished in May this year. 10 months for a simple yes/no!
Yikes...that's a big exponent to be testing! 10 months...I wonder how soon
before we all end up testing in that range...
Of course, it would be nice to actually find one, but I work with computers
all the time and for some odd reason, it strikes me as nearly criminal that
all those CPU cycles are being wasted. US WEST spent millions on all new
machines and NT to run on 'em, and they only use them for dumb
terminals...running X-Windows emulators to access mainframe stuff.
In any given day, the "idle" cycle on the boxes would have about 23:45,
meaning the CPU was only in use 15 minutes. Thus my unusual quote, taken
out of context and printed in the papers, that "...all that computational
power was too tempting for me." It really was too tempting... :-) But
some folks just don't get it I guess...sigh...
For what it's worth, a friend of mine on the inside recently told me that
the problems that US WEST had that led to their discovery of the program
was only affecting a handful of machines, i.e. less than 10.
I suspect some machines were acting up, as NT boxes sometimes will, and the
first thing they noticed on all the machines was some unusual process
called NTPRIME.EXE. It was showing near 100% cpu time so they freaked I'm
sure and soon discovered it running on other machines.
It's unusual though that they imply that all 2500 machines in their Phoenix
center were affected when the original problem was almost certainly related
to something else and was only seen on a small number of PC's... Dagnabit!
:-(
Aaron
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From: Lars Soezueer <[EMAIL PROTECTED]>
Date: Mon, 08 Mar 1999 11:04:51 +0100
Subject: Mersenne: Re: Alien stuff
[EMAIL PROTECTED] wrote:
> 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.)
There have been many attempts to construct such languages.
I am not aware of any of these projects to be
especially designed for communication with aliens.
What I do know is that one of them has actually developed
into a living spoken language,
and the Web Pages of GIMPS are even available
in a translation to it:
http://try.physik.uni-erlangen.de/~soezueer/pr/prime/prime.html
"Ted prenis libron antauxhieraux, kaj rapide legis gxin.
Ted pensis ke la libro estis tre informa."
Lars
- --
Lars S"oz"uer |Tel.: +49-9131-33351 private
Schornbaumstr. 4 | >>>NEW>>>: -85-27066 office
D-91052 Erlangen |FAX: -15249
Germany |e-mail: [EMAIL PROTECTED]
Web Site: http://try.physik.uni-erlangen.de/~soezueer
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From: Henrik Olsen <[EMAIL PROTECTED]>
Date: Mon, 8 Mar 1999 15:54:46 +0100 (CET)
Subject: Re: Mersenne: biiiiig perfect number
On Sun, 7 Mar 1999, Spike Jones wrote:
> I once had a great idea: I would express the Great Number in hex!
> Then I realized that I would get with 4 pages of tiny Fs. {8-[
> Not so interesting. But if some clever GIMPSer were to generate the
> perfect number that is (M37*(M37+1))/2 then express *that* number
> in hex, I would clear off a space on my office wall for it. {8-] Anyone
> accept the challenge?
Lots of F's, followed by one fewer 0's, not a lot prettier. :)
- --
Henrik Olsen, Dawn Solutions I/S
URL=http://www.iaeste.dk/~henrik/
Get the rest there.
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From: "Mauricio J. A. Latorre A." <[EMAIL PROTECTED]>
Date: Mon, 08 Feb 1999 12:31:33 +0400
Subject: Re: Mersenne: mersennes for exocivilizations
I, as exociticen, is not very impressed with a large string filled with a
lot of 1�s and 0�s, can be a numerical serie, it�s similar to the "Moon
Lisa", but can be just static, or just a barbarian exocivilization that
only use 1 and 0.
Maybe we must send sorted numbers (0 to n) to set a numerical system,
followed by operations between numbers (2, 4, 6, .... m*2 .... n ) for
plus, (2,4,8,16,...2^m, ..., n) etc...
Mauricio -=\Chubasco/=- Latorre
At 06:54 PM 07-03-1999 -0500, you wrote:
>One problem that seems hidden in transmitting a large Mersenne numbers is
>the difficulty in decoding a very long string
>of binary 1's. Apart from a constant signal being non-random, how does a
>receiver know when it starts and stops? And
>how do they guess how to parse it.
>
>I hate to paraphrase a comic, but compared to a Cobol core-dump, Joan
>Rivers', "Can we talk?" is easily understood.
>
>Sending Mersennes looks like a singularly difficult way to get somebody's
>attention.
>
>Joth Tupper
>
>________________________________________________________________
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>
>
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From: Jud McCranie <[EMAIL PROTECTED]>
Date: Mon, 08 Mar 1999 11:41:19 -0500
Subject: Re: Mersenne: biiiiig perfect number
>>I once had a great idea: I would express the Great Number in hex!
About 20 years ago I wrote a program to tabulate and print Mersenne primes
in base 10. Then I thought "Hey, they are very simple in a base that is a
power of 2 - just do a base conversion!" So I did that, and to my
surprise, the two programs took almost exactly the same amount of time to
run. Then I realized that what they were actually doing was essentially
the same (although the base conversion was a more complex program).
+------------------------------------------+
| Jud McCranie [EMAIL PROTECTED] |
+------------------------------------------+
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From: [EMAIL PROTECTED]
Date: Mon, 8 Mar 1999 09:07:40 -0800 (PST)
Subject: Re: Mersenne: Moo?
What about windowing the data? Only utilize a certain portion of it at a
time. It would be highly complex, although I don't see why a computer
couldn't keep track of it.
Is there anyone who can do any theoretical calculations on what this would
gain for us?
- -Chuck
On Sun, 7 Mar 1999, Clayton Smith wrote:
> >Yes, it would take an enormous amount of RAM to do this, but what if we
> >stored the data in some kind of compressed format (a ZILLION to 1
> >compression???), or some kind of reference format? Then we could take
> >advantage of everyone's clock cycles used on other searches. There's got
> >to be a way of virtually referencing somthing that is not able to exist.
> >Look at the way we use a MOD instead of the actual number.
> >
> >Just some ramblings...
>
>
> If we compressed the data by any constant factor (e.g. a zillion), the
> amount of data to be stored would still double with each squaring, so we'd
> be not much better off.
>
> Suppose we had sufficient memory available to do the computation. How long
> would it take? Assume we've discovered something better than FFT and can
> multiply in O(n) time (as far as I know, this is the best that can be done
> since you have to at least look at the whole number). Each S(n) is twice
> the length of the previous one, and the squarings would take O(2^n) time. 1
> + 2 + 2^2 + ... 2^(n-1) = 2^n, so the whole computation would take O(2^n)
> time. That's a lot of time! And of course, actually dividing M(n) into
> S(n-2) would take just about as long.
>
> - Clayton
>
>
--
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From: "James Smith" <[EMAIL PROTECTED]>
Date: Mon, 8 Mar 1999 17:20:30 -0000
Subject: Re: Mersenne: Re: Alien stuff
I could be wrong, but that looks like Esperanto to me.
- --
James Smith
[EMAIL PROTECTED]
>What I do know is that one of them has actually developed
>into a living spoken language,
>and the Web Pages of GIMPS are even available
>in a translation to it:
>http://try.physik.uni-erlangen.de/~soezueer/pr/prime/prime.html
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From: "Michael Bell" <[EMAIL PROTECTED]>
Date: Mon, 8 Mar 1999 20:47:46 -0000
Subject: Re: Mersenne: mersennes for exocivilizations
>
> The above is a steadily increasing sequence, which could be used to
advantage.
> One could represent delta n for additional compression.
> 1,1,1,1,2,1,1,3,7,6,4,3,67,12,... has fewer bits.
> Then put the message through something standard like Huffman or LZH.
> The difficulty is that with each step the message becomes more obscure.
> And the essence of a message is to communicate something.
>
Surely if we just wanted to communicate, just a list of primes would be
enough to distinguish our message from random signals. We would surely
only be worrying about trying to impress our ET neighbours once contact had
been established, I vote we send out 2,3,5,7,11,13,...
Michael.
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From: "Ernst W. Mayer" <[EMAIL PROTECTED]>
Date: Mon, 8 Mar 1999 16:26:07 -0500
Subject: Mersenne: Printout of M3021377
Several people have mentioned a decimal printout of M3021377.
Richard Crandall's PSI site (www.perfsci.com) has a nice poster
of precisely that number, and I'm sure it looks a lot better
than several loose sheets of white paper. $7.95 doesn't seem
outrageous...
- -Ernst
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From: David L Nicol <[EMAIL PROTECTED]>
Date: Mon, 08 Mar 1999 17:35:56 -0600
Subject: Re: Mersenne: *P*M3021377 in base 62
Spike Jones wrote:
>
> > spike wrote: ... if some clever GIMPSer were to generate the
> > >perfect number that is (M37*(M37+1))/2 then express *that* number
> > >in hex, I would clear off a space on my office wall for it. {8-]
>
> Clayton Smith wrote:
>
> > The binary expansion of this number will be p 1's followed by p-1
> > 0's. In hex it would be equally boring.
No, it be %100 more interesting, having four characters instad of
just two: a 3, 755343 Fs, an E, and 755344 0s.
> On second thought, maybe it is good to use base 62
as long as your base isn't a power of two you'll get a curious grey
texture; the next edition of my business card is going to be handwritten
in black marker across part of prime3.ps (at an angle)
> Then yahoos could search for more proof that Elvis loves them
> in *P*M3021377
> 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.
No, that won't work at all because every base64 encoder I've
ever seen relies on bit-shifting, and you'll need to mod the whole thing
by your odd base on every character-producing pass. It would be a nice
test of an arbitrary-precision arithmatic package.
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From: "Robert G. Wilson v, PhD ATP" <[EMAIL PROTECTED]>
Date: Mon, 08 Mar 1999 18:49:09 -0600
Subject: Re: Mersenne: mersennes for exocivilizations
[EMAIL PROTECTED] wrote:
> In a message dated 3/6/99 9:22:49 PM Eastern Standard Time, [EMAIL PROTECTED]
> writes:
>
> > 1, 2, 3, 4, 6, 7, 8, 11, 18, 24, 28, 31, 98, 111, 207, 328, 339, 455, 583,
> > 602,
> > 1196, 1226, 1357, 2254, 2435, 2591, 4624, 8384, 10489, 12331, 19292, 60745,
> > 68301, 97017, 106991, 215208, 218239, ... , .
> >
>
> Okay, now what if we get a sequence like this:
>
> 5, 9, 10, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 25, 26, 27, 29, 30, 32,
> ...., 97, 99, 100, ...
>
> ________________________________________________________________
> Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
That's just the compliment of the former. Easy.
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From: Jason Stratos Papadopoulos <[EMAIL PROTECTED]>
Date: Mon, 8 Mar 1999 20:03:27 -0500 (EST)
Subject: Re: Mersenne: Mersenne Processor
On Sun, 7 Mar 1999 [EMAIL PROTECTED] wrote:
>
> If one were to build a microprocessor SPECIFICALLY suited to LL testing,
> what would the assembly instruction set look like? Approximately what
> would the architecture look like? Speed shouldn't be an issue because
> there's never enough anyway and we're trying to work smarter not harder.
For floating point FFTs: Get all the memory bandwidth you can,
build a large cache, make it non-blocking on a cache miss. Allow
prefetching. Double precision floating point (53-bit IEEE is enough),
superscalar execution, separate pipelined FPU add and multiply units
would be nice. Nothing else is necessary in the FPU, other than
register moves.
For integer FFTs: get yourself a good n-bit to 2n-bit multiply, pipeline
it if you have to but make it real fast. Superscalar is also nice, but
memory bandwidth isn't as important because you can get away with a
smaller array to store the data in.
Making a standard risc ALU instruction set (the 3-operand kind) would
be nice also.
Unfortunately, I just described the UltraSPARC, the Alpha and the PII.
If you *insist* on a do-it-yourself job, look into Analog Devices'
SHARC line of DSP chips, they kick butt for high-bandwidth integer math.
jasonp
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End of Mersenne Digest V1 #524
******************************
