Mersenne Digest Saturday, July 31 1999 Volume 01 : Number 607
----------------------------------------------------------------------
Date: Thu, 29 Jul 1999 13:36:37 -0600
From: "Aaron Blosser" <[EMAIL PROTECTED]>
Subject: RE: Mersenne: Average Machines
> 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.
Without trying to think to hard about your estimate, I'll just pitch in by
saying it might be useful to count the number of computers who've checked in
recently (the past 2 months or so?) just to get an idea of how many of those
computer accounts are actually still running.
Primenet probably keeps track of every account/computer that ever
participated, regardless of whether it is *still* participating (although I
think the number in the status page shows only computers with an exponent
checked out).
A quick glance through the stats pages show that many accounts are long
overdue (about to expire their exponents). Presumably these are folks who
joined GIMPS and got bored or something and removed it. Oh well.
So I'm guessing the actual number of computers *still running* a GIMPS
client is less than what you used in your calculations.
Aaron
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Date: Thu, 29 Jul 1999 14:39:28 -0600
From: "Blosser, Jeremy" <[EMAIL PROTECTED]>
Subject: RE: Mersenne: STOP BASHING PEOPLE WITH SLOWER MACHINES! (Stop th e madness!)
Noooooooooooooo not again!
BTW, we'd place higher if Primenet credited out account for the work my
UltraEnterprise4000 and RS/6000 are doing... Is this ever going to change or
is this a permanent thing where only x86 clients get credit?
Oh, and I compiled MacLucasUNIX with Sun's C compiler instead of GCC and got
about a 100% speed increase, I suggest other Solaris users do the same. :)
(I get some .5s/iter on the crappy 167mhz CPUs which is about par w/ a
P233MMX)
- -Jeremy
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Date: Thu, 29 Jul 1999 17:28:03 -0400
From: "Rick Pali" <[EMAIL PROTECTED]>
Subject: RE: Mersenne: Better to wait?
From: Yvan Dutil
> 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.
Of course everyone's personal point of view on this will depend on their own
hardware, but I started in pre-Primenet days with a P100 and now have a
P400...and the time to complete an exponent has significantly increased.
I set my 400 and 200 to double checking because I kinda like having numbers
finish in about 5 and 10 days respectively again. :-)
Rick.
- -----
[EMAIL PROTECTED]
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Date: Thu, 29 Jul 1999 18:38:20 EDT
From: [EMAIL PROTECTED]
Subject: Mersenne: Re: Mo' moolah
Lucas Wiman wrote:
>Even if they (George and Scott) did this, then there would
>still be MacLucasUNIX, or everything else in the mers package, as well as
>Ernst's program, and good ol' lucas.c. Any of these could be used. We've
>really got to put our feet back on the ground here. If we did put a license
>change on all of George's program derivitives, we would still have to get
>Will and Ernst to change their copyrights, and Richard Crandall.
In fact, I've been thinking about these issues for some months now.
I already have GNU-style copyleft language in the upcoming release of Mlucas,
but the monetary issue complicates things. My personal view is, if I spent
a lot of time and wrote the program, I should be entitled to a share of the
money (and being between jobs at the moment, it would come in handy :)
But, how does one combine that with a copyleft? If I give you the right to
to freely modify and redistribute my code (with original header intact) that
would seem to imply any associated prize money split percentages remain in
force, but at what point (i.e. many modifications later, say 5 years after
I put it out there and others pick it up and I'm killed by a freak asteroid
impact on my way home from the Coffee Society) does it cease to be my code
in any legally enforceable sense. And, to my knowledge, the whole issue of
a copyleft has never been subjected to a serious legal challenge, so its
legal status is unclear.
>From an algorithmic/prime finding perspective, I don't want to be too greedy,
since fewer people will want to run my code if they get only 10% of any money
(let's face it, that's human nature), nor do I want to put too strict a clamp
on the source code, since I want to encourage algorithmic improvements,
assembly
implementation, interfacing with a PrimeNet GUI, etc., all those things which
need others' input and effort, even if I'm still closest to the basic
algorithm
at the heart of the thing.
As in so many other arenas, money is nice to have, but it can really
complicate
matters.
>In fact, is the DWT patented?
Crandall and Fagin published the details in 1994 in Math. Comp., which
(I believe) precludes any patenting. Had they patented it first, they
would be licensing others to use it, meaning that the EFF money would
likely not be an issue, since GIMPS would not have gotten started without
free software for all to use.
Aaron Blosser wrote:
>And it was mentioned before...if George and/or Scott setup such a legal
>contract regarding software usage, there probably would be people writing
>their own software, hoping to get the big cash all to themselves.
I think Aaron understimates the amount of work it takes to write a really
good program of this kind. Even $100000 would not reimburse George for
his work on Prime95, at any reasonable hourly wage for a skilled programmer.
And even if you've written a great code, you need to get *lots* of people
to run it - insisting on keeping any prize money for yourself makes you
seem greedy, and it's that perception more than anything else that would
hurt your recruiting.
- -Ernst
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------------------------------
Date: Thu, 29 Jul 1999 19:05:39 EDT
From: [EMAIL PROTECTED]
Subject: Mersenne: And for for something completely unrelated
<<Apollos 11, 12, 14, 15, 16 and 17 each landed (two men out of a crew
of three).>>
Auuugh, I can't count. 12 men HAVE landed, silly me. But Americans can still
spell better. :-D
S.T.L.
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Date: Thu, 29 Jul 1999 19:34:20 EDT
From: [EMAIL PROTECTED]
Subject: Mersenne: Cut the Crap!
Can we cut the crap on this list? Better yet, can we have
another mailing list that is just announcements? The threads
are getting ridiculous. I switched to "digest", but I'm afraid I'll
miss the one important announcement among the 100 pieces
of less useful email.
- --
Randy Given
[EMAIL PROTECTED]
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public key at http://members.aol.com/GivenRandy/pgpkey.asc
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Date: Thu, 29 Jul 1999 20:44:08 -0400 (EDT)
From: Lucas Wiman <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Cut the Crap!
> Can we cut the crap on this list?
Hear, Hear! Especially the neo-poaching thread. This is simply too
volatile and pointless a thread to waste our time on.
Quite frankly, I'm also getting kind of annoyed with "When do you think
we will see a [power of ten] digit prime?" type questions also, though
some of the subtreads have been interesting.
> Better yet, can we have another mailing list that is just announcements?
Interesting idea, and one that makes sense for those who have less time on
their hands.
It seems almost like the FAQ has reduced math on the list and increased
pointless "prediction" questions.
Though of course I am probably just confusing correlation with causation.
- -Lucas
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------------------------------
Date: Thu, 29 Jul 1999 17:48:26 -0700
From: "Joth Tupper" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Cut the Crap! [Or is that Can the Spam?]
When I got back from vacation, I had about 300 messages from Mersenne. Some
I tossed based on sender, some on topic, but a most I just skimmed. Sure, I
probably missed something I care about, but only you can figure out what you
care about.
If you think it is off topic, feel free to take it private or even reply to
the sender.
I find that a lot of the off-topic discussions have interesting bits in them
that I sometimes find useful.
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Date: Thu, 29 Jul 1999 20:17:37 -0700
From: Luke Welsh <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Re: Mo' moolah
At 06:38 PM 7/29/99 EDT, Ernst Mayer wrote:
>>In fact, is the DWT patented?
>
>Crandall and Fagin published the details in 1994 in Math. Comp., which
>(I believe) precludes any patenting. Had they patented it first, they
>would be licensing others to use it, meaning that the EFF money would
>likely not be an issue, since GIMPS would not have gotten started without
>free software for all to use.
Had there been no George Woltman, a "GIMPS" would have started anyway,
albeit with much inferior (and non-DWT) code. George got there first,
and he got it right the first time.
Follow-ups to soc.history.what-if
- --Luke
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------------------------------
Date: Fri, 30 Jul 1999 11:26:12 +0200
From: Paul Landon <[EMAIL PROTECTED]>
Subject: Mersenne: Telling people to FAQ Off.
Please don't be so quick to tell people to "FAQ Off" or an equivalent.
Any barriers to newbies joining in is a barrier to the exponential
growth of GIMPS.
I would like to see more communication on this subject and whilst
some of the Maths is beyond me and some of the Computing is
beneath my interest, my keyboard has a PageDown and a Delete
key.
I find GIMPS and this mailing list interesting because it helps me
learn more Maths.
> 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 must admit that I haven't done even the elementary reading, yet I still
find this topic interesting.
Actually I have read a couple of books on Elementary Number Theory
and I can't remember this. (This is not a proof that the subject wasn't in
those books :-)
> 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".
>
OK, I will. Is there a Web page about this? ;-)
>
> Is there a Web page about this ?
>
> ** Does everything have to be on the Web?
>
That would be nice.
> Have people gotten too lazy to use
> a
> library?
>
No. I like libraries.
Within arms reach I have multiple sessions to one of the fastest internet
links in the world.
Conversely I do not know of an accessible English Language good Maths
library near Nuremberg.
>
> Is this could be of any use in the search for large primes ?
>
Valid question.
The answer is probably "No", but it is a valid question.
Cheers,
Paul Landon
ps. How about one of the more knowledgeable Mathematicians (or Computer
Scientists) regularly communicating a little tutorial on an interesting subject
of
their choosing?
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Date: Fri, 30 Jul 1999 15:38:10 +0200
From: Sturle Sunde <[EMAIL PROTECTED]>
Subject: Re: Mersenne: STOP BASHING PEOPLE WITH SLOWER MACHINES! (Stop th e madness!)
> Oh, and I compiled MacLucasUNIX with Sun's C compiler instead of GCC and got
> about a 100% speed increase, I suggest other Solaris users do the same. :)
> (I get some .5s/iter on the crappy 167mhz CPUs which is about par w/ a
> P233MMX)
This is normal. Expect a greater speed increase on the RS/6000, if you use
IBM's C-compiler with automatic profiling feedback.
Expect a significant speed increase from GCC on Sparc with the -mv8 option.
(Without it GCC emulates the multiply instruction...)
- --
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: Fri, 30 Jul 1999 18:51:38 +0100
From: "Brian J. Beesley" <[EMAIL PROTECTED]>
Subject: Mersenne: Pepin's Test, etc.
Given that x^2 mod 2^p-1 can be computed very efficiently using DWT
(getting the remaindering operation for free), it occurs to me that
it ought to be possible to compute x^2 mod 2^p+1 just as efficiently,
using different "magic numbers". So, although Pepin's Test looks very
like Proth's Test (the only other difference is that using the base 3
is always sufficient for testing Fermat numbers), it _should_ be
possible to write an implementation of Pepin's Test that is about as
efficient as Prime95.
The problems are, of course, that there are going to be very few
Fermat numbers which can be tested in a "reasonable" time given
"current" hardware (by _any_ definition of the words quoted), and
that there is a very small chance that any of them will turn out to
be prime.
In case anyone else notices that F25 is an "interesting" size -
10,100,891 digits - could I save you a whole bundle of time by
remarking that F25, F26 and F27 are all known to be composite, we
know at least one factor of each of them. And F28 isn't quite big
enough to be worth $150K.
...............................................
On 30 Jul 99, at 11:26, Paul Landon wrote:
> Please don't be so quick to tell people to "FAQ Off"
Yes, I agree. Lots of replies like this on the list get irritating,
even to those of use who aren't the target of the abuse.
I suggest that those who feel it neccessary to reply in this vein do
so privately to the questionner, something along the lines of "There
is a FAQ at URL <> which answers your question : <quote from FAQ>"
The point here is that it keeps the list quieter, gives the
questionner the information they want and gently leads them to the
FAQ. And it's really no more effort than sending a "FAQ off" reply to
the list.
Regards
Brian Beesley
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Date: Fri, 30 Jul 1999 19:39:42 -0700
From: "Terry S. Arnold" <[EMAIL PROTECTED]>
Subject: Mersenne: Win 2000 & FAT32
Does Win 2000 Beta 3 work with FAT32?
Terry S. Arnold 2975 B Street San Diego, CA 92102 USA
[EMAIL PROTECTED] (619) 235-8181 (voice) (619) 235-0016 (fax)
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Date: Sat, 31 Jul 1999 00:33:07 -0400
From: "Chris Nash" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Telling people to FAQ Off.
Hi Paul...
<and others whose names I will not mention, they know who they are. and they
should know better too>.
> Please don't be so quick to tell people to "FAQ Off" or an equivalent.
> Any barriers to newbies joining in is a barrier to the exponential
> growth of GIMPS.
Wholeheartedly agree here. Lucas Wiman made a wonderful job of the FAQ - but
not *every* question is in there... if it were, what would be the point of
having a mailing list anyway? Or is, as Paul says, the list meant to be a
forum for people to shoot down every well-meaning question just because
they're farther up the learning curve? Some of Paul's examples are
blatant...
> > - - - 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??
So this is a "waste of time" is it? Is <this poster> trying to say that
getting interested in number theory is a waste of time? Furthermore, if
<this poster> had such a grasp of this "simple and well-understood" fact,
he'd realize there was no need to be rude about it. This might be
"elementary", but who's to say there's something in it that has been
overlooked for centuries? And despite its supposedly elementary nature,
"cycle lengths" of sequences are the basis of EVERY classical primality
test.
I would hate to be so arrogant to believe I knew everything about a subject.
I'd much rather have one well-meaning newbie poster than a dozen
self-opinionated ones. This sort of interest serves the most precious
purpose of all, it gets new people into the subject? Who cares if it's been
done before, or known for centuries? It might be something new to the
poster... it might just be their entrance into this beautiful subject.
My 8-year old is fascinated that she can multiply by 9, add the digits up,
and get back to 9 again. Perhaps I should take the above villain's advice,
tell her she is wasting her time, and ignore her completely. I think not.
> > What is it that causes people NOT to do even elementary reading first?
Perhaps the clue is in the poster's question? That he is worried about his
English? These "elementary" questions on this list fall into three
categories:
(1) there are a number of results that are already known, or easily
deducible from known theorems;
(2) there are results which, so far as I know, are new and interesting, but
interesting rather from their curiosity and apparent difficulty than their
importance;
(3) there are results which appear to be new and important...
As Lucas Wiman recently said to me (off-list, and I hope he doesn't mind me
quoting it), what if Hardy had instead said, "This Indian fellow is not
worth my time?".
> > 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".
OK, off scurries our interested neophyte. He finds "Lagrange's theorem" and
is somewhat perturbed. How on earth does it help him that the order of a
subgroup divides the order of a group? Congratulations, all-knowing poster,
for deterring our interested number theorist...
> > Have people gotten too lazy to use
> > a library?
Have people *become* too lazy to give a civil answer to the interested
poster? If you don't wish to answer, then don't bother. If you do but feel
it's off-topic, do so off-list. Let's wonder too whether the poster was too
lazy to think of a grammatically-correct equivalent of *gotten* as well, no,
I'm not being a pointy hair, this was after all an answer to someone for
whom American English is not their primary language.
> No. I like libraries.
> Within arms reach I have multiple sessions to one of the fastest internet
> links in the world.
> Conversely I do not know of an accessible English Language good Maths
> library near Nuremberg.
I love this concept, books are great. The web is great. The fact that
someone who knows the answer will see your question is wonderful. Perhaps
people need to think what this list is about. Perhaps people need to
re-analyse their reasons for being on it. If they're on it to discourage the
interested, then they're better off somewhere else.
> > Is this could be of any use in the search for large primes ?
> Valid question.
> The answer is probably "No", but it is a valid question.
The answer is definitely "yes", since all classical primality tests are
equivalent to finding the cycle length of an expansion in some base.
> ps. How about one of the more knowledgeable Mathematicians (or Computer
> Scientists) regularly communicating a little tutorial on an interesting
subject
> of their choosing?
It would be a great idea, provided of course the know-it alls could stand
it. Yes, I'm backing Paul up here. I'm annoyed the way things periodically
go on here. I'm annoyed that, once in a while, someone comes out and shoots
down another for either 1) having a slower computer 2) not having 20 years
of mathematical education, or 3) being interested enough to ask a sensible
question.
Here is a fictitious posting. If you recognize it, great. If anyone wants to
answer it, wonderful - I will find a suitable prize for the first person who
considers this "a waste of time"...
Dear Sirs,
I would like to tell you about a remarkable primality proof I have been
working on. There is little space here for me to include all the details,
but my proof does not require mechanical devices, merely a reasonable amount
of human labor. With the aid of several hundred grains of rice laid out on
the squares of chessboards, I am capable of calculations involving large
numbers. By this method, I plan to find the largest prime number of our
time.
Those who recognize it, please, just smile about it.
Chris Nash
Lexington KY
UNITED STATES
==================================================
Please Note: my e-mail address is now [EMAIL PROTECTED]
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Date: Sat, 31 Jul 1999 03:12:44 -0400 (EDT)
From: Lucas Wiman <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Telling people to FAQ Off.
> Lucas Wiman made a wonderful job of the FAQ - but not *every* question
> is in there... if it were, what would be the point of having a mailing
> list anyway?
Nor should every question be in there. I wrote the FAQ to promote
*interesting* mathematical discussion, and prevent rehash of the same
questions every couple of weeks.
Besides, where do we draw the line? "Why can't people read back issues
of Math. Comp. from 1930?"
> Or is, as Paul says, the list meant to be a
> forum for people to shoot down every well-meaning question just because
> they're farther up the learning curve?
I understand the frustration with people who ask "simplistic" questions,
I mean I wrote the FAQ for goodness sake. But if a question is that
annoying to you, delete the message and let others (who have more
patience) field the question. Don't waste your obviously quite valuable
time with such an intellectually lazy simpleton.
> > *** Why? The mathematics is simple and well understood and has been
known
> > for centuries. Did you check the literature first, before wasting your
> > time??
I find that often to understand something fully, I must derive the theorem
on my own. I don't know why that is, but remember not everyone learns
by reading endless books about theory.
> My 8-year old is fascinated that she can multiply by 9, add the digits up,
> and get back to 9 again. Perhaps I should take the above villain's advice,
> tell her she is wasting her time, and ignore her completely. I think not.
An excellent point!
> As Lucas Wiman recently said to me (off-list, and I hope he doesn't mind me
> quoting it), what if Hardy had instead said, "This Indian fellow is not
> worth my time?".
I don't mind a bit.
> Those who recognize it, please, just smile about it.
HaHaHaHaHaHa! :)
- -Lucas
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Date: Sat, 31 Jul 1999 08:24:16 -0500 (CDT)
From: Chris Caldwell <[EMAIL PROTECTED]>
Subject: Mersenne: A possible venue for a GIMPS meeting
One of these lists: Primes-L or Mersenne, had mentioned having folks get
together at a number theory meeting. The third of these below might be
the ideal time--if folks were still interested we could contact the
organizors and arrange a session (I would be willing to). For example,
depending on interest, we could try to arrange talks on the history of
primes and Mersenne finding, or a panel discussion of
GIMPS/PrimeNets/Proth's future, papers on the basic heuristics of prime
searching... Since Primes-L/GIMPS both include folks at all levels of
math, there is room for a very wide variety of presentations. It would be
fun to organize these session(s).
=========
The University of Illinois at Urbana-Champaign is having a "Special Year
in Number Theory 1999/2000" which involves having a number of long term
visitors, and several meetings: (See http://www.math.uiuc.edu/nt2000/ )
Illinois Number Theory Conference, September 17-18, 1999
"One hour talks will be given by K. Alladi, P. Borwein, A. Pollington,
and K.S. Williams. There will be opportunity for about 20 contributed
talks." No registration fee.
Midwest Arithmetical Geometry in Cryptography Workshop, November 5 - 7,
1999
"This workshop is intended for people in academia and industry with a
basic mathematical background in group theory and number theory, wishing
to learn about the increasingly common applications of arithmetical
geometry to cryptography. The featured speakers are Neal Koblitz, Joe
Silverman, and Nigel Smart, each of whom will give three hour talks. There
will also be time for contributed talks."
(This one:)
*** Millennial Conference on Number Theory, May 21 - 26, 2000 ****
"Confirmed plenary speakers include G. Andrews, J. Coates, H. Darmon,
K. Ford, R. Graham, A. Granville, D.R. Heath-Brown, C. Hooley, W.-C. Li,
K. Murty, M. Nathanson, K. Ono, C. Pomerance, W. Schmidt, C. Skinner, K.
Soundararajan, R. Taylor, R. Tijdeman, and R.C. Vaughan. Several of the
plenary talks will be in the form of broadly accessible survey lectures.
Proceedings will be published."
AMS Sectional Meeting at Urbana, March 18 - 21, 1999
"We expect that around 70 talks at this meeting will be in number
theory."
Instructional Conference on Fermat's Last Theorem, Summer 2000
===
Postscript:
"Good" number theory meetings are relatively common, but this
"Millennial Conference" looks like it will be exceptional. The list of
speakers is already very impressive and they will have "broadly accessible
survey lectures" (though that couuld mean many things...) Because of that,
it may be worth folks going to the expense to come. What do you think?
Should we try to organize something?
Chris Caldwell
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Date: Sat, 31 Jul 1999 10:52:54 -0400
From: Jud McCranie <[EMAIL PROTECTED]>
Subject: Re: Mersenne: A possible venue for a GIMPS meeting
At 08:24 AM 7/31/99 -0500, Chris Caldwell wrote:
"Good" number theory meetings are relatively common, but this
>"Millennial Conference" looks like it will be exceptional.
Perhaps it will be the equivalent for the next millennium of Hilbert's 1900
talk was for this century (giving his 23 problems)!
+----------------------------------------------+
| Jud "program first and think later" McCranie |
+----------------------------------------------+
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Date: Sat, 31 Jul 1999 09:13:54 -0600
From: "Aaron Blosser" <[EMAIL PROTECTED]>
Subject: RE: Mersenne: Win 2000 & FAT32
> Does Win 2000 Beta 3 work with FAT32?
Not exactly a Mersenne question, but yes.
Ob. GIMPS reference:
I've been running NTPrime on Win2000 for about a year now (since it was NT5,
various builds) and it runs splendidly. No worries.
Aaron
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Date: Sat, 31 Jul 1999 12:22:12 +0100
From: Tony Forbes <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Pepin's Test, etc.
"Brian J. Beesley" <[EMAIL PROTECTED]> writes
>In case anyone else notices that F25 is an "interesting" size -
>10,100,891 digits - could I save you a whole bundle of time by
>remarking that F25, F26 and F27 are all known to be composite, we
>know at least one factor of each of them.
The cofactor of F25 (after dividing out all the known factors) is
currently 'status unknown', isn't it?.
So it might be worth testing for compositeness. However at present there
seems to be no way of proving it prime if it fails the compositeness
test.
- --
Tony
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Date: Sat, 31 Jul 1999 11:57:35 +0100
From: Tony Forbes <[EMAIL PROTECTED]>
Subject: Re: Mersenne: STOP BASHING PEOPLE WITH SLOWER MACHINES!
Sturle Sunde <[EMAIL PROTECTED]> writes
>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.)
The problem I have with slow computers is that I cannot afford to run
them. A 40MHz 486 uses about 20 Watts, a 400MHz AMDK6 about 40 Watts.
However if you have your own hydroelectric power supply, or if someone
else is paying the electricity bill, the situation is different.
- --
Tony
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Date: Sat, 31 Jul 1999 13:02:33 -0400
From: Chip/Sandy Kerchner <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Pepin's Test, etc.
>
> The cofactor of F25 (after dividing out all the known factors) is
> currently 'status unknown', isn't it?.
>
> So it might be worth testing for compositeness. However at present there
> seems to be no way of proving it prime if it fails the compositeness
> test.
Tony,
Actually the status of F24 is unknown. F25 has three known factors.
F25 = (48413*2^29 +1)(1522849979*2^27+1)(16168301139*2^27+1)*C33554349
If Pepin's primality test was run on F24, we could determine if F24 was
composite or prime. The chances that F24 is a psuedo-prime (a composite
pretending to be a prime) are very slim so it is worth the time to run the
test. I estimate the time required would be 6-9 months and we could do it with
existing software.
Chip Kerchner
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Date: Sat, 31 Jul 1999 16:08:38 -0400 (EDT)
From: Lucas Wiman <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Pepin's Test, etc.
> If Pepin's primality test was run on F24, we could determine if F24 was
> composite or prime. The chances that F24 is a psuedo-prime (a composite
> pretending to be a prime) are very slim so it is worth the time to run the
> test. I estimate the time required would be 6-9 months and we could do it
> with existing software.
Pepin's test on Fermat numbers is deterministic. There is no such thing as a
Pepin psuedo-prime Fermat number.
- -Lucas
P.S. Shouldn't this discussion be on Primes-L?
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End of Mersenne Digest V1 #607
******************************
