Delivered-To: luke@ndatech.com X-Sender: rugeley@pop3.demon.co.uk X-Mailer: QUALCOMM Windows Eudora Version 5.1 Date: Sat, 15 Dec 2001 22:44:42 +0000 To: Luke Welsh From: mersenne-digest-invalid-reply-address@base.com (Mersenne Digest) (by way of Gordon Spence ) Subject: Mersenne Digest V1 #913
Mersenne Digest       Tuesday, December 4 2001       Volume 01 : Number 913

----------------------------------------------------------------------

Date: Sun, 02 Dec 2001 19:57:25 +0000
From: Gordon Spence <gordon@rugeley.demon.co.uk>
Subject: Mersenne: Re: Mersenne Digest V1 #912

It was previously written....

>From: "Steve Harris" <steve@sheeplechasers.org>
>Subject: Re: Mersenne: Re: Factoring benefit/cost ratio
>
>George did say that, and I was aware of his statement, but that still has no
>effect on the point I was making.
>George's GIMPS stats also give no credit at all for finding factors,

Tell me about it, over 150,000 and no mention anywhere....

It was also written....

>Date: Sun, 2 Dec 2001 18:55:57 -0000
>From: bjb@bbhvig.uklinux.net
>Subject: Re: Mersenne: Re: Factoring benefit/cost ratio
>
>On 1 Dec 2001, at 17:39, George Woltman wrote:
>
> > This is because my rather limited reporting software only adds up the
> > LL results in the verified and one-LL-tests databases. Once an
> > exponent is factored it is removed from those databases.
>
>The other problem here is that the "known factors" database does
>not include the discoverer.

A particularly sore point. If we maintained a top "savers" list whereby for
every factor found you were credited with the time an LL test would have
taken, then I and the other "Lone Mersenne Hunters" would pulverise these
big university teams.

150,000 factors in the 60-69m range, at an average of 27.2 P-90 years each
- - hmmmm just over 4,000,000 years saved....

regards

Gordon

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------------------------------

Date: Mon, 3 Dec 2001 07:25:39 -0000
From: bjb@bbhvig.uklinux.net
Subject: Re: Mersenne: Re: Mersenne Digest V1 #912

On 2 Dec 2001, at 19:57, Gordon Spence wrote:

> >From: "Steve Harris" <steve@sheeplechasers.org>
> >
> >George did say that, and I was aware of his statement, but that still has no
> >effect on the point I was making.
> >George's GIMPS stats also give no credit at all for finding factors,
>
> Tell me about it, over 150,000 and no mention anywhere....

Ah, but George's GIMPS stats encourage factoring by removing LL
testing credit when a factor is subsequently found. (Either you
should have done more factoring before you started LL testing, or
the factoring you did was expensive!)

> >From: bjb@bbhvig.uklinux.net
> >
> >The other problem here is that the "known factors" database does
> >not include the discoverer.
>
> A particularly sore point. If we maintained a top "savers" list whereby for
> every factor found you were credited with the time an LL test would have
> taken, then I and the other "Lone Mersenne Hunters" would pulverise these
> big university teams.

Umm... let's put it this way. Who gets the credit for finding the
factor 2p+1 when p+1 is divisible by 4 and both p & 2p+1 are
prime? That's a _big_ bunch of numbers ... I'm not sure that there
are an infinite number of 3 mod 4 Sophie Germain primes, but there
certainly are a _lot_ of them... and I think you have to credit them
all to the person who proved the theorem.
>
> 150,000 factors in the 60-69m range, at an average of 27.2 P-90 years each
> - hmmmm just over 4,000,000 years saved....

With due respect, I don't think it's entirely reasonable to award
credit for more effort than was actually expended, or for more effort
than it would have taken to run two LL tests.

I think some realistic formula for finding the factor 2kp+1 would look
like:

            k>=2^64   2 x LL test CPU time
2^63 <= k < 2^64   1 x LL test CPU time
2^62 <= k < 2^63   0.5 x LL test CPU time
2^61 <= k < 2^62   0.25 x LL test CPU time
etc etc

_provided_ that no credit was given for factoring work which failed
to find a factor.

However there are clearly philosophical differences here as well as
practical ones - what Gordon says is clearly absolutely true in the
literal sense.

Possibly the best idea is the simplest - leave the current
procedures alone!

Regards
Brian Beesley
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------------------------------

Date: Mon, 03 Dec 2001 03:29:24 -0500
From: Nathan Russell <nrussell@acsu.buffalo.edu>
Subject: Re: Mersenne: Re: Mersenne Digest V1 #912

At 07:57 PM 12/2/2001 +0000, Gordon Spence wrote:
>A particularly sore point. If we maintained a top "savers" list whereby
>for every factor found you were credited with the time an LL test would
>have taken, then I and the other "Lone Mersenne Hunters" would pulverise
>these big university teams.

Should George get credit for eliminating all those composite exponents when
he made his initial list in the mid-1990's?

He probably found over a dozen times as many composites in (at a guess)
under two minutes than we'll EVER find, at least until the project is
extended past 80M.

Nathan

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------------------------------

Date: Mon, 3 Dec 2001 15:48:32 +0100
From: =?utf-8?Q?Torben_Schl=C3=BCntz?= <Torbens@friendtex.dk>
Subject: SV: Mersenne: Re: Mersenne Digest V1 #912

No you wouldn't because they would like yourself go to do only
factoring work, and as George said to me when I propose this a year ago:
It would make the focus of GIMPS towards factoring and not like it is
now on primenumber finding.
We will (again in "George-words") have to eliminate candidates
by using a small amount of time in the factoring field; but only so
much/less that we still have power to run LL-tests to really prove
primes.

Regards and happy hunting
tsc

        A particularly sore point. If we maintained a top "savers" list
whereby for
        every factor found you were credited with the time an LL test
would have
        taken, then I and the other "Lone Mersenne Hunters" would
pulverise these
        big university teams.

150,000 factors in the 60-69m range, at an average of 27.2 P-90
years each
- hmmmm just over 4,000,000 years saved....

regards

Gordon

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------------------------------

Date: Mon, 03 Dec 2001 12:50:31 EST
From: EWMAYER@aol.com
Subject: Mersenne: Re: need access to an SGI

Whoops - when I wrote the original message, I forgot that
the source tarball for Mlucas 2.7c is still in the build
area of the ftp archive - it hasn't yet been promoted to
the release area. You can get it at

ftp://hogranch.com/pub/mayer/junk/Mlucas_2.7c.tar.gz

- -Ernst

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------------------------------

Date: Mon, 03 Dec 2001 13:58:44 EST
From: EWMAYER@aol.com
Subject: Mersenne: Re: SF Bay area GIMPS party

OK, the San Francisco Bay area GIMPS get-together will
take place this coming Friday, 7. December, in the south
bay area (precise venue to be decided soon - see below.)
Any GIMPS participant or Mersenne prime fan is welcome
to join us, along with anyone else you'd like to bring -
this is not a formal party.For those not coming from the San Jose area, the venue
will be close to a Caltrain station, and hence should be
reachable from e.g. SFO airport or other outlying areas.
I'm also going to try to arrange what ridesharing I can,
so if you can provide a ride or need a ride, please let
me know. I looks like several folks from far-flung places
will be attending, so should be a quite interesting
company. Alas, Luke Welsh can't attend, but he suggested
several venues, two of which form my short list.

1) Tied House, Mountain View
2) Faultline Brewery, Sunnyvale

1) is very close to a Caltrain station; 2) supposedly
has very good food. Luke also mentioned the Tied House
in downtown San Jose, but I've heard it's often very
crowded and not as easy in terms of public transit access
as the one in Mountain View.

So, if you plan to attend and have been to both places
(I've not been to (2)), your preference would be most
valuable. I hope to finalize the location this afternoon,
so out-of-towners will have a reasonable amount of time
to make their plans.

Since the proverbial M#39 cat is out of the proverbial
bag, the guess-the-new-Mersenne-prime-exponent contest
is officially cancelled. I was hoping to have a prime
poster signed by all the attendees to give to the winner,
but I don't think they'll be ready by then, anyway.

Cheers,
- -Ernst

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------------------------------

Date: Mon, 3 Dec 2001 11:07:13 -0800
From: "John R Pierce" <pierce@hogranch.com>
Subject: Mersenne: Re: SF Bay area GIMPS party

> 1) Tied House, Mountain View
> 2) Faultline Brewery, Sunnyvale

either, orther, as far as I care... heh.

re: ride sharing, I have a new 7 passenger van, and might be able to carpool
folks from the Santa Cruz area... assuming I can go (I've got to check with
SWMBO to make sure we don't have a prior engagement on that date).

- -jrp

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------------------------------

Date: Mon, 3 Dec 2001 20:45:46 -0000
From: "Daran" <darang@lineone.net>
Subject: Re: Mersenne: Re: Factoring benefit/cost ratio

- ----- Original Message -----
From: "George Woltman" <woltman@alum.mit.edu>
To: "Gerry Snyder" <gerrysnyder@mediaone.net>; <mersenne@base.com>
Sent: Saturday, December 01, 2001 10:39 PM
Subject: Re: Mersenne: Re: Factoring benefit/cost ratio

> I prefer a factor to a double-check. But it is hard to quantify "prefer"
in a
> mathematical formula for computing trial factoring limits. Prime95 uses
> the formula:   cost_of_factoring must be less than
chance_of_finding_a_factor
> times 2.03 * the cost_of_an_LL_test.

Shouldn't that be 1.015 for double-checking assignments?

Also does the cost part of the calculation recognise the increased cost of
trial-factorisation after 2^64?

I've noticed on occasion that I've had to do an extra round of trial
factoring before proceeding with an doublecheck. This indicates that
previous factorisation has been non-optimal, or have the estimates for the
relative costs of factoring vs. LL testing changed with the introduction of
new hardware?

Finally if P-1 factorisation were to be spun off into a separate work unit,
then the optimal arangement would be to trial factor while
cost_of_trial_factoring * chance_of_P-1_factoring is less than
cost_of_P-1_factoring * chance_of_trial_factoring. Then P-1 factorise.
Then complete trial factorisation according to the above formula.

> -- George

Daran G.

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Date: Mon, 3 Dec 2001 20:45:58 -0000
From: "Daran" <darang@lineone.net>
Subject: Re: Mersenne: M#39 news!

- ----- Original Message -----
From: <bjb@bbhvig.uklinux.net>
To: <mersenne@base.com>
Sent: Saturday, December 01, 2001 8:02 PM
Subject: Re: Mersenne: M#39 news!

> ...I would have expected
> George's initial announcement to say "over 4 million digits" rather
> than "well over 3.5 million digits" (which would nevertheless be
> true!).

Or he might have said "nearly 4 million digits" which would also have been
true.

> Of course I could simply be misreading George's mind -
> possibly if he had said "over 4 million" it would have narrowed the
> field sufficiently to make identification easy.

I fear that this may be the case, given what various people have been able
to dig out of what has been said.

[...]

> I would strongly suggest that procedures are changed so that the
> next time a Mersenne prime is discovered, no information at all is
> released except to prior discoverers of Mersenne primes...

As a matter of interest, why should prior discoverers be so privileged?

[...]

> Irritated

Yes, I rather feel the same. It's like enjoying the build-up to Christmas
only to find that someone's open your present five days ahead of time.

> Brian Beesley

Daran G.

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------------------------------

Date: Mon, 3 Dec 2001 23:22:28 -0000
From: bjb@bbhvig.uklinux.net
Subject: Re: Mersenne: Re: Factoring benefit/cost ratio

On 3 Dec 2001, at 20:45, Daran wrote:

> Shouldn't that be 1.015 for double-checking assignments?

I think 1.03. However you do have a point. P-1 limits do depend on
the trial factoring depth, and are much smaller for DC assignments
than for first tests, so there is already something "built in".
>
> Also does the cost part of the calculation recognise the increased cost of
> trial-factorisation after 2^64?

Yes. The trial factoring depth is constant at 64 bits from ~8.5
million to ~13 million. Don't forget that the number of candidates
which need to be checked is _inversely_ proportional to the
exponent.
>
> I've noticed on occasion that I've had to do an extra round of trial
> factoring before proceeding with an doublecheck. This indicates that
> previous factorisation has been non-optimal, or have the estimates for the
> relative costs of factoring vs. LL testing changed with the introduction of
> new hardware?

I think the latter has something to do with it - PPro is about twice
as efficient at factoring compared with LL testing as a plain
Pentium. This is because of much improved pipeline organization
including the provision of spare registers enabling speculative
execution, which greatly increased the throughput of the floating
point unit in particular.

Another factor is that early versions of the program were unable to
factor as deep as current versions.
>
> Finally if P-1 factorisation were to be spun off into a separate work unit,
> then the optimal arangement would be to trial factor while
> cost_of_trial_factoring * chance_of_P-1_factoring is less than
> cost_of_P-1_factoring * chance_of_trial_factoring. Then P-1 factorise.
> Then complete trial factorisation according to the above formula.

Interesting - but I think the effect would be small.

What about factoring to a "fractional" depth? With a roughly
logarithmic distribution of factors, surely about half the factors
between 2^n and 2^(n+1) would be smaller than 2^(n+0.5), whilst
searching to 2^(n+0.5) would take only about 41% of the time
taken to search the whole interval.

Regards
Brian Beesley
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Date: Mon, 3 Dec 2001 20:38:43 -0600 (CST)
From: ribwoods@execpc.com
Subject: Re: Mersenne: Re: Factoring benefit/cost ratio

Responses to a couple of postings --

Steve Harris wrote:
> Actually, Richard's statement that "a 'Factored' status is better
> for GIMPS than a 'Two LL' status" is not quite true. It's better for
> the mathematical community as a whole,

"Better for the mathematical community as a whole" is actually almost
exactly what I had in mind when I started composing that paragraph
... honest! But then I started revising, and lost some stuff in the
process.

Nevertheless, I stand by my assertion that "a 'Factored' status is
better for GIMPS than a 'Two LL' status" ... insofar as our LL testing
remains less reliable than our factor verification. Double-checking
certainly improves LL result reliability, but I think our record shows
that a verified factor is still slightly (by a minute but nonzero
margin) more reliable an indicator of compositeness than two matching
nonzero LL residues.

(See earlier discussions of potential reasons for incorrect LL
results.
Some error sources would be more likely to affect the longer LL test
than the shorter factor verification.)

> It matters to those who are attempting to fully factor Mersenne
> numbers, but that's a different project altogether,

Some of us like to participate in both. :-)

> and one that is decades (at least) behind GIMPS. The only reason we
> do any factoring at all is to reduce the time spent on LL testing.

But if factoring is not really part of GIMPS's purpose (and I agree it
isn't), how can a separate factoring effort be "behind" GIMPS at all?
Aren't they measuring their progress in a different, non-comparable,
dimension?

> Besides, if you do manage to find a 75-digit factor of a
> 2-million-digit Mersenne number, that still leaves a 1999925-digit
> remainder. Really not much help :-)

"A journey of a thousand miles begins with but a single step."

Two million three-foot steps total more than one thousand miles.

- - - - - -

In reply to a statement of mine about "the extra benefit of finding a
specific factor",
Daran G. wrote:
>I can see no way of objectively quantifying this benefit.

Well -- if there's no objective quantification of the extra benefit of
finding a specific factor, then it seems to me that there's no
objectively quantifiable justification for saying that it's not
valuable to do a certain amount of "extra" P-1 factoring on a
once-LL'd Mnumber. :)

In response to my writing:
>> This reflects the view (with which I agree) that it is more
valuable
>> to know a specific factor of a Mnumber than to know that a Mnumber
is
>> composite but not to know any specific factor of that Mnumber.
>>
>> So a "Factored" status is better for GIMPS than a "Two LL" status,
but
>> calculations of factoring benefit that consider only the savings of
>> L-L test elimination are neglecting the difference between those
two
>> statuses. If one consciously wants to neglect that difference ...
>> well, okay ... but I prefer to see that explicitly acknowledged.
Daran G. wrote:
>It seems to be implicitely acknowledged in the way the trial
factoring
>depths are determined.

But don't forget that this refers to a depth determined by Prime95
_in the context of calculating the factoring tradeoff point for
maximizing GIMPS throughput for the "Test=" worktype_, NOT the context
of a "Factor=" or "Pminus1=" worktype where the user has explicitly
specified factoring limits, possibly for reasons beyond the ken of
Prime95.

Daran continues:
> If one places a non-zero value on a known factor, then the utility
> of extra factoring work on untested, once tested, and verified
> composites would be increased.

Yes.

But that doesn't have to affect Prime95's calculation of tradeoff
points _for maximizing throughput of the "Test=" worktype_.

I'm not saying that Prime95 should incorporate into its calculations a
nonzero value for the benefit of finding a specific factor.

I'm saying that it is rational for someone to decide to factor past
the Prime95-calculated tradeoff points, and that it is unjustified to
criticize "extra" factoring on the grounds that going past the
Prime95-calculated tradeoff points is wasted effort.

Richard B. Woods

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Date: Mon, 03 Dec 2001 18:45:58 -0800
From: Luke Welsh <luke@ndatech.com>
Subject: Re: Mersenne: M#39 news!

At 08:45 PM 12/3/01 -0000, Daran wrote:
At 08:02 PM 12/1/01 -0000, Brian Beesley wrote:
>> I would strongly suggest that procedures are changed so that the
>> next time a Mersenne prime is discovered, no information at all is
>> released except to prior discoverers of Mersenne primes...
>
>As a matter of interest, why should prior discoverers be so privileged?

Various reasons, but elitism not one of them.

One of the reasons is to provide an opportunity to offer advice to the new
discoverer on how to handle the publicity... what kinds of, umm, "insightful"
questions the press might ask... and which answers are likely to make it
into print.

- --Luke, who *still* manages to look foolish

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Date: Mon, 03 Dec 2001 22:14:54 -0500
From: George Woltman <woltman@alum.mit.edu>
Subject: Mersenne: Re: M#39 news

Hi all,

        Mersenne mailing list readers were treated to unexpected sneak-peek
at the new Mersenne prime's exponent.

        Science magazine heard of the discovery and contacted Scott and I.
Since Science magazine is one of the two most widely read science-oriented
magazines, we felt it would be a good opportunity. Because of longish
lead times in the magazine publishing industry, we took a calculated risk
and gave them a draft of the press release with the understanding that
specific details should be withheld until confirmation is
official. Unfortunately,
this did not happen.

        This was an unintentional mistake for which the author has
sincerely apologized. The on-line article has been corrected. Fortunately,
word has not spread too widely and it seems this slip-up will not interfere
with an orderly announcement later this week.

        Press coverage is always a "wild card". The quality and number of
news stories depend on many factors including the author's knowledge and
interest, editor's pen, space considerations, other news, time since last prime
found, whether an interesting "angle" can be promoted, etc.

        M#35 got good coverage with the "PC bests supercomputer angle".
M#36 got swamped by Princess Diana's death. M#37 didn't make too big
a splash. M#38 got decent coverage because of the EFF award. M#39 -
time will tell.

        I don't see any great reason to change our announcement policies.
The premature article on slashdot may even have been beneficial as
several reporters have contacted us rather than us having to go out and
drum up interest.

Have fun,
George

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Date: Mon, 03 Dec 2001 22:41:18 -0500
From: George Woltman <woltman@alum.mit.edu>
Subject: Re: Mersenne: Re: Factoring benefit/cost ratio

At 08:38 PM 12/3/2001 -0600, ribwoods@execpc.com wrote:
>Nevertheless, I stand by my assertion that "a 'Factored' status is
>better for GIMPS than a 'Two LL' status"

I think everyone is in agreement on this.

>But if factoring is not really part of GIMPS's purpose (and I agree it
>isn't),

I think of GIMPS as two projects. The larger project is "let's find the
next Mersenne prime". The much smaller project is "let's maximize our
knowledge of all Mersenne numbers".

>I'm saying that it is rational for someone to decide to factor past
>the Prime95-calculated tradeoff points,

I agree. I've done several P90 CPU years of that myself.

I think more of the discussion has centered around stats and the
formula for picking how far to trial factor, rather than whether factoring
is of some mathematical value. I'm not inclined to change the trial
factoring formula. If I recall correctly, when I last computed the formula
I erred on the side of more factoring rather than less. As to the stats,
maybe, just maybe, we can upgrade our stats system in 2002. I
know from other distributed projects that many users are fanatical
about any changes in stats. We will have to tread very carefully!

- -- George

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Date: Tue, 4 Dec 2001 07:44:12 -0000
From: bjb@bbhvig.uklinux.net
Subject: Re: Mersenne: Re: Factoring benefit/cost ratio

On 3 Dec 2001, at 20:38, ribwoods@execpc.com wrote:

[... snip ...]
> Nevertheless, I stand by my assertion that "a 'Factored' status is
> better for GIMPS than a 'Two LL' status" ... insofar as our LL testing
> remains less reliable than our factor verification. Double-checking
> certainly improves LL result reliability, but I think our record shows
> that a verified factor is still slightly (by a minute but nonzero
> margin) more reliable an indicator of compositeness than two matching
> nonzero LL residues.

AFAIK our record does _not_ show any such thing. In _theory_
there is a very small chance that we _may_ have accepted an
incorrect residual even after double-checking. There is a small
chance in such a case that the residual should have been zero, i.e.
we missed a Mersenne prime.

I've triple-checked thousands of small exponents - some of the
ones where the accepted residual was recorded to only 16 bits or
less, which makes the chance of an undetected error _much_
greater (though still quite small) - so far no substantive errors in the
database have come to light. A very few (think fingers of one hand)
instances of incorrectly matched residuals have come to light -
completing the double-check in these cases proved that one of the
recorded residuals was correct.

[... snip ...]
> Some error sources would be more likely to affect the longer LL test
> than the shorter factor verification.)

Indeed - if errors occur at random intervals, results should get less
reliable as runs take progressively longer. However there does
seem to be a wide variation in the reliability of systems. Some
seem to have a lot of problems, some very few (if any).

I've detected four problems on my own systems so far; two of these
were caused by a failed cooling fan on a P100 system (unlike
current systems, the cooling was _almost_ sufficient even without
forced ventilation); one was caused by a configuration error -
running Glucas on an Alpha system I inadvertently allowed "fast"
arithmetic and turned off error checking, which was a really stupid
thing to do on a system with a 53-bit mantissa FPU - as this was a
QA run on a 33 million range exponent, I was lucky to lose only 3
months work. The last one I never got to the bottom of, but I
strongly suspect that Prime95's workspace memory was clobbered
during a software installation on a Windows 98 system.
>
> > It matters to those who are attempting to fully factor Mersenne
> > numbers, but that's a different project altogether,
>
> Some of us like to participate in both. :-)
>
> > and one that is decades (at least) behind GIMPS. The only reason we
> > do any factoring at all is to reduce the time spent on LL testing.
>
> But if factoring is not really part of GIMPS's purpose (and I agree it
> isn't), how can a separate factoring effort be "behind" GIMPS at all?
> Aren't they measuring their progress in a different, non-comparable,
> dimension?

Indeed.

There is still a distinction between finding a factor - _any_ factor
will do, it doesn't even matter if you find a composite factor which
you can't break down further - which eliminates the need to run a
LL test in order to eliminate a Mersenne number as a candidate
prime, and finding all the factors (or even just the smallest factor) of
a Mersenne number.
>
> > Besides, if you do manage to find a 75-digit factor of a
> > 2-million-digit Mersenne number, that still leaves a 1999925-digit
> > remainder. Really not much help :-)

(Aside - we're rather more likely to find a 75-bit factor than a 75-
digit factor. In fact, finding a 75-digit prime factor of a "no factors
known" Mersenne number with an exponent under 80 million would
be a significant achievement in itself. The slip doesn't alter the
author's argument.)

At the moment, having found one factor, we quit. That's sufficient
effort for the purpose of trying to find Mersenne primes. A little
more work might break the cofactor down further.

Attempting to test the primality of the cofactor - even using PRP
rather than a stringent test - would be interesting, but would
unfortunately be about as expensive as running the LL test that
we've managed to avoid!

> [ big snip ]
> I'm saying that it is rational for someone to decide to factor past
> the Prime95-calculated tradeoff points, and that it is unjustified to
> criticize "extra" factoring on the grounds that going past the
> Prime95-calculated tradeoff points is wasted effort.

It's rational for someone to have fun. If they want to factor past the
Prime95-calculated tradeoff points, that's fine. Even better if they
record their unsuccessful efforts, so that other people don't waste
time searching the haystack for the needle that isn't there.

There is another point here. We _can_ (by trial factoring, and at a
cost) eliminate at least some prime candidates from the class of
Mersenne numbers which are so large that we will _never_ be able
to LL test them - not even if the whole Universe was a computer,
with storage density of one bit per fundamental particle!

By a logical extension of this argument, in _this_ Universe there
are three classes of natural numbers - not just a distinction
between prime and composite - there are also at least some
numbers (an infinite number of them, in fact) which we will never be
able to factor or to prove prime by purely computational means,
because the storage required is greater than the Universe can
provide.

The challenge is to push the lower bound of this class of numbers
as high as possible.

Regards
Brian Beesley
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Date: Mon, 3 Dec 2001 14:53:59 -0000
From: Keith Garland <Keith.Garland@arklife.ie>
Subject: Mersenne: New exponents

Hi from Ireland - I have a few questions about how M39 will affect the
allocation of current/new exponents. Once the result has been announced I
suppose we will recommence searching above M39? I got a couple of new
exponents over the weekend - I assume that they are not necessarily > M39 in
order to maintain "secrecy". If so then, after the announcement, should we
dump our existing tests or finish off factoring things that are half
finished? Does prime95 handle this scenario automatically - i.e. will new
exponents be automatically sent if a manual update is done?

Thanks,

Keith

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Date: Tue, 4 Dec 2001 01:19:21 -0800
From: "Paul Leyland" <pleyland@microsoft.com>
Subject: RE: Mersenne: Re: Factoring benefit/cost ratio

> From: bjb@bbhvig.uklinux.net [mailto:bjb@bbhvig.uklinux.net]

>
> (Aside - we're rather more likely to find a 75-bit factor than a 75-
> digit factor. In fact, finding a 75-digit prime factor of a
> "no factors
> known" Mersenne number with an exponent under 80 million would
> be a significant achievement in itself.

Finding a 75-digit prime and non-algebraic factor of any integer with
more than, say, 200 digits would be a significant achievement. The
record today is 55 digits; it reached 53 digits 3 years ago and only a
handful of factors with 50 or more digits have been found ever. I have
precisely one of them to my credit 8-)

> At the moment, having found one factor, we quit. That's sufficient
> effort for the purpose of trying to find Mersenne primes. A little
> more work might break the cofactor down further.

Actually, some of us don't quit. But we're a small bunch of weirdos,
and we only work on tiny exponents anyway.

Paul
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Date: Tue, 04 Dec 2001 10:19:46 -0500
From: George Woltman <woltman@alum.mit.edu>
Subject: Re: Mersenne: New exponents

Hi Keith,

At 02:53 PM 12/3/2001 +0000, Keith Garland wrote:
>Hi from Ireland - I have a few questions about how M39 will affect the
>allocation of current/new exponents. Once the result has been announced I
>suppose we will recommence searching above M39?

The GIMPS project is dedicated to finding ALL Mersenne primes within
reach of today's computers. The server will continue to hand out the
smallest available exponents without regard for M39.

If you find a new prime smaller than M39, you have found something *really*
rare - an out-of-order Mersenne prime. Only one of those as ever been found
when Welsh and Colquitt found M110503. Some argue that M4253 was
found out-of-order, but the computer discovered it in-order....

Most new assignments will be above M39 anyway, but if you only
want world-record candidates and the server sends you a small one
then send me an email and I'll email you a bigger one to test. I'll also
add your suggestion to the program's wish list.

Best regards,
George

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Date: Tue, 04 Dec 2001 11:48:32 -0500
From: Nathan Russell <nrussell@acsu.buffalo.edu>
Subject: Re: Mersenne: New exponents

At 10:19 AM 12/4/2001 -0500, George Woltman wrote:

>If you find a new prime smaller than M39, you have found something *really*
>rare - an out-of-order Mersenne prime. Only one of those as ever been found
>when Welsh and Colquitt found M110503. Some argue that M4253 was
>found out-of-order, but the computer discovered it in-order....

For the information of the list, the folks who *want* to try to get
exponents below (the presumed) M#39 might want to look into manually
fetching work at 2:00 (IIRC) in the morning Eastern standard (7 or 8 GMT),
when the server releases exponents of folks who have stopped participating
without properly quitting. You face a small risk that the original tester
will submit a result, but even in that case you'll get credit for the
double-check (though that would be a small consolation if a prime were
found).

Nathan

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Date: Tue, 4 Dec 2001 10:01:59 -0800
From: "John R Pierce" <pierce@hogranch.com>
Subject: Re: Mersenne: Re: SF Bay area GIMPS party

> > 1) Tied House, Mountain View
> > 2) Faultline Brewery, Sunnyvale
>
> either, orther, as far as I care... heh.
>
> re: ride sharing, I have a new 7 passenger van, and might be able to
carpool
> folks from the Santa Cruz area... assuming I can go (I've got to check
with
> SWMBO to make sure we don't have a prior engagement on that date).

SWMBO says 'sure'.

So... anyone in the Santa Cruz area wants a ride up and back, let me know by
friday. I could haul as many as 6 extra folks in reasonable comfort (I
gotta brand new Ford E150 complete with leather quad captains chairs).

Can I assume we've decided to stick with the Mtn View Tied House? Has a
time been set? I'd suggest 7pm-ish for dinner.

- -jrp

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Date: Tue, 4 Dec 2001 19:03:45 +0100
From: Jan Munch Pedersen <jmp@vejlehs.dk>
Subject: SV: Mersenne: New exponents

This message is in MIME format. Since your mail reader does not understand
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> If you find a new prime smaller than M39, you have found
> something *really*
> rare - an out-of-order Mersenne prime. Only one of those as
> ever been found
> when Welsh and Colquitt found M110503. Some argue that M4253 was
> found out-of-order, but the computer discovered it in-order....

M61, M89, and M107 were also out-of-order.

Best wishes
Jan

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> If you find a new prime smaller than M39, you have found
> something *really*
> rare - an out-of-order Mersenne prime. Only one of those as
> ever been found
> when Welsh and Colquitt found M110503. Some argue that M4253 was
> found out-of-order, but the computer discovered it in-order....

M61, M89, and M107 were also out-of-order.

Best wishes
Jan
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End of Mersenne Digest V1 #913
******************************