Mersenne Digest Sunday, May 13 2001 Volume 01 : Number 849
----------------------------------------------------------------------
Date: Sat, 12 May 2001 08:06:41 +0200
From: [EMAIL PROTECTED] (Achim Passauer)
Subject: Mersenne: missing exponents?
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Hi all,
I was a bit astonished this morning (0500 UTC) when I saw that about =
50.000 exponents have been cleared since the last database synch. A few =
days ago there were about 53.000 to 54.000 of them. Were have 3.000 to =
4.000 exponents gone? Any explanation?
Regards
Achim
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<META content=3D"MSHTML 5.50.4522.1800" name=3DGENERATOR></HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT size=3D2>Hi all,</FONT></DIV>
<DIV><FONT size=3D2></FONT> </DIV>
<DIV><FONT size=3D2>I was a bit astonished this morning (0500 UTC) when =
I saw that=20
about 50.000 exponents have been cleared since the last database synch. =
A few=20
days ago there were about 53.000 to 54.000 of them. Were have 3.000 to =
4.000=20
exponents gone? Any explanation?</FONT></DIV>
<DIV><FONT size=3D2></FONT> </DIV>
<DIV><FONT size=3D2>Regards<BR>Achim</FONT></DIV></BODY></HTML>
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------------------------------
Date: Sat, 12 May 2001 10:35:46 +0200
From: "Dieter Schmitt" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: missing exponents?
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Hi Achim,
have a look a the available exponents for double checking.
George has made several thousend new exponents available. Maybe the new =
exponents hadn't been double checked before or previous double checking =
results didn't match. Therefore he had to do a 'small synchronization' =
at some ranges to remove older double checking results.
Regards
Dieter
-----Urspr=FCngliche Nachricht-----=20
Von: Achim Passauer=20
An: [EMAIL PROTECTED]=20
Gesendet: Samstag, 12. Mai 2001 08:06
Betreff: Mersenne: missing exponents?
Hi all,
I was a bit astonished this morning (0500 UTC) when I saw that about =
50.000 exponents have been cleared since the last database synch. A few =
days ago there were about 53.000 to 54.000 of them. Were have 3.000 to =
4.000 exponents gone? Any explanation?
Regards
Achim
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charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
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<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Diso-8859-1">
<META content=3D"MSHTML 5.50.4522.1800" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT size=3D2>Hi Achim,</FONT></DIV>
<DIV><FONT size=3D2></FONT> </DIV>
<DIV><FONT size=3D2>have a look a the available exponents for double=20
checking.</FONT></DIV>
<DIV><FONT size=3D2></FONT> </DIV>
<DIV><FONT size=3D2>George has made several thousend new exponents=20
available. Maybe the new exponents hadn't been double checked =
before=20
or previous double checking results didn't match. Therefore he =
had to=20
do a 'small synchronization' at some ranges to remove older double =
checking=20
results.</FONT></DIV>
<DIV><FONT size=3D2></FONT> </DIV>
<DIV><FONT size=3D2>Regards</FONT></DIV>
<DIV><FONT size=3D2>Dieter</FONT></DIV>
<DIV><FONT size=3D2></FONT> </DIV>
<BLOCKQUOTE dir=3Dltr=20
style=3D"PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; =
BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style=3D"FONT: 10pt arial">-----Urspr=FCngliche Nachricht----- =
</DIV>
<DIV=20
style=3D"BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: =
black"><B>Von:</B>=20
<A [EMAIL PROTECTED]=20
href=3D"mailto:[EMAIL PROTECTED]";>Achim Passauer</A> </DIV>
<DIV style=3D"FONT: 10pt arial"><B>An:</B> <A =
[EMAIL PROTECTED]=20
href=3D"mailto:[EMAIL PROTECTED]";>[EMAIL PROTECTED]</A> </DIV>
<DIV style=3D"FONT: 10pt arial"><B>Gesendet:</B> Samstag, 12. Mai 2001 =
08:06</DIV>
<DIV style=3D"FONT: 10pt arial"><B>Betreff:</B> Mersenne: missing=20
exponents?</DIV>
<DIV><FONT size=3D2></FONT><FONT size=3D2></FONT><FONT =
size=3D2></FONT><FONT=20
size=3D2></FONT><FONT size=3D2></FONT><BR></DIV>
<DIV><FONT size=3D2>Hi all,</FONT></DIV>
<DIV><FONT size=3D2></FONT> </DIV>
<DIV><FONT size=3D2>I was a bit astonished this morning (0500 UTC) =
when I saw=20
that about 50.000 exponents have been cleared since the last database =
synch. A=20
few days ago there were about 53.000 to 54.000 of them. Were have =
3.000 to=20
4.000 exponents gone? Any explanation?</FONT></DIV>
<DIV><FONT size=3D2></FONT> </DIV>
<DIV><FONT =
size=3D2>Regards<BR>Achim</FONT></DIV></BLOCKQUOTE></BODY></HTML>
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------------------------------
Date: Sat, 12 May 2001 12:33:49 +0200
From: [EMAIL PROTECTED] (Achim Passauer)
Subject: Re: Mersenne: missing exponents?
Hi all again,
Dietmar, thanks for your answer. Well that might be an explanation but to
move thousands of exponents from the cleared list to the still-to-do-list
would also mean a major setback, wouldn�t it? And I�d highly appreciate to
be informed about that by Entropia or George.
Regards
Achim
PS: sorry that my last mail was HTML, hope that this is pure ASCII
again.........
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Date: Sat, 12 May 2001 13:14:00 +0200
From: mohk <[EMAIL PROTECTED]>
Subject: Re: Mersenne: missing exponents?
At 12:33 12.05.2001, you wrote:
>Hi all again,
>
>Dietmar, thanks for your answer. Well that might be an explanation but to
>move thousands of exponents from the cleared list to the still-to-do-list
>would also mean a major setback, wouldn�t it? And I�d highly appreciate to
>be informed about that by Entropia or George.
>
>Regards
>Achim
>
>PS: sorry that my last mail was HTML, hope that this is pure ASCII
>again.........
You should use another MailClient as Microsoft Outlook Express 4.72.3110.1 8)
Didn't you read all the bad things about Mailwurms etc?
regards,
Mohk
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------------------------------
Date: Sat, 12 May 2001 13:28:36 +0200
From: Martijn Kruithof <[EMAIL PROTECTED]>
Subject: Re: Mersenne: missing exponents?
Achim Passauer wrote:
> Hi all again,
>
> Dietmar, thanks for your answer. Well that might be an explanation but to
> move thousands of exponents from the cleared list to the still-to-do-list
> would also mean a major setback, wouldn�t it? And I�d highly appreciate to
> be informed about that by Entropia or George.
>
> Regards
> Achim
>
> PS: sorry that my last mail was HTML, hope that this is pure ASCII
> again.........
All exponents are tested twice, this also means they appear twice in the
cleared stats, so if 1000 1st time checked exponents are released for
double checks the cleared since last sync stats for primenet go down by
1000 and this is in that case not a major setback (not a setback at
all), that figure goes down when database syncs take place and when
first time checked exponent ranges are released for double check,
strictly speaking the figure going down by a large value frequently
shows that we are making major progress! (The number should more or less
remain constant)
Martijn
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------------------------------
Date: Sat, 12 May 2001 12:50:40 +0100 (BST)
From: Chris Jefferson <[EMAIL PROTECTED]>
Subject: Re: Mersenne: missing exponents?
>
> You should use another MailClient as Microsoft Outlook Express 4.72.3110.1 8)
> Didn't you read all the bad things about Mailwurms etc?
Sorry, I just felt the urge to say this. There is nothing particualarily
bad about Outlook Express, these various viruses require you to excute
attachments, and you can do that in any mail client.. If any other mail
client gets as popular as OE, then it will start to have viruses aimed at
it's address book too!
Chris
> > regards, >
> Mohk
>
>
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------------------------------
Date: Sat, 12 May 2001 10:22:06 -0400
From: George Woltman <[EMAIL PROTECTED]>
Subject: Re: Mersenne: missing exponents?
Hi all,
At 12:33 PM 5/12/2001 +0200, Achim Passauer wrote:
>Dietmar, thanks for your answer. Well that might be an explanation but to
>move thousands of exponents from the cleared list to the still-to-do-list
>would also mean a major setback, wouldn�t it? And I�d highly appreciate to
>be informed about that by Entropia or George.
Dietmar's guess was accurate. Six weeks ago there were grumblings on the
list that we were making slow progress on double-checking milestones. I
promised to make monthly checks of my database and the server's database
and make exponents available for triple-checking when necessary.
I did this yesterday. Not all exponents are triple checks, some were exponents
that were never added to the servers list of exponents to double-check.
Why did this affect the server's counts? Well, that's a long story. It has to
do with design decisions (compromises actually) made at Primenet's inception.
Primenet's database is a subset of the master database which I maintain
3000 miles away from the server. In an ideal world there would only be one
database maintained by the server and all database maintenance (like
triple-checks) would be handled automatically.
To make matters worse, Primenet was not originally designed to
hand out double-checking assignments. This has resulted in some minor
glitches, especially when double-checking and first-time checking ranges
overlap.
Scott/Entropia gave me a simple tool to do some remote server database
maintenance. I can schedule triple-checks by essentially telling the server
to forget about the double-check result it already has.
This is not a setback for the project. To get accurate counts of the master
database, visit http://www.mersenne.org/status.htm. There you will see
that 157,484 exponents have been double-checked and 127,720 exponents
have been tested once.
Hope that helps,
George
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Date: Sat, 12 May 2001 11:27:34 -0400
From: Jud McCranie <[EMAIL PROTECTED]>
Subject: Re: Mersenne: missing exponents?
At 10:22 AM 5/12/2001 -0400, George Woltman wrote:
>Dietmar's guess was accurate. Six weeks ago there were grumblings on the
>list that we were making slow progress on double-checking milestones. I
>promised to make monthly checks of my database and the server's database
>and make exponents available for triple-checking when necessary.
Checking the status page, we seem to be stuck on 26 exponents between
6,325,000 and 6,972,593 - that haven't had one LL test. I've been double
checking exponents in this range for months (and getting them done at the
rate of more than 1 per month). I've been double checking because that is
"work makes the most sense", but does it make sense to double check this
range when there are untested ones? If these 26 were actually being
tested, they would be knocked off at the rate of at least one per day, and
it has been a while since one has been finished.
+------------------------------------+
| Jud McCranie |
| |
| former temporary part-time adjunct |
| instructor of a minor university |
+------------------------------------+
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------------------------------
Date: Sat, 12 May 2001 16:52:07 +0100 (BST)
From: Chris Jefferson <[EMAIL PROTECTED]>
Subject: Re: Mersenne: missing exponents?
>
> Checking the status page, we seem to be stuck on 26 exponents between
> 6,325,000 and 6,972,593 - that haven't had one LL test. I've been double
> checking exponents in this range for months (and getting them done at the
> rate of more than 1 per month). I've been double checking because that is
> "work makes the most sense", but does it make sense to double check this
> range when there are untested ones? If these 26 were actually being
> tested, they would be knocked off at the rate of at least one per day, and
> it has been a while since one has been finished.
Haven't we had enough discussions about taking bnumbers people are takingf
a long time to test / not chexcking uin very often? :)
Chris
>
>
>
>
> +------------------------------------+
> | Jud McCranie |
> | |
> | former temporary part-time adjunct |
> | instructor of a minor university |
> +------------------------------------+
>
>
> _________________________________________________________________________
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Date: Sat, 12 May 2001 12:05:14 -0400
From: Nathan Russell <[EMAIL PROTECTED]>
Subject: Re: Mersenne: missing exponents?
On Sat, 12 May 2001 11:27:34 -0400, Jud McCranie wrote:
>At 10:22 AM 5/12/2001 -0400, George Woltman wrote:
>
>>Dietmar's guess was accurate. Six weeks ago there were grumblings on the
>>list that we were making slow progress on double-checking milestones. I
>>promised to make monthly checks of my database and the server's database
>>and make exponents available for triple-checking when necessary.
>
>Checking the status page, we seem to be stuck on 26 exponents between
>6,325,000 and 6,972,593 - that haven't had one LL test.
Doesn't that most likely mean that those exponents have been checked
out, and allowed to expire, multiple times?
Nathan
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Date: Sat, 12 May 2001 12:41:59 -0400
From: Jud McCranie <[EMAIL PROTECTED]>
Subject: Re: Mersenne: missing exponents?
At 04:52 PM 5/12/2001 +0100, Chris Jefferson wrote:
>Haven't we had enough discussions about taking bnumbers people are takingf
>a long time to test / not chexcking uin very often? :)
Sorry if that has been covered, but I just got back on the list after being
off for several months.
+------------------------------------+
| Jud McCranie |
| |
| former temporary part-time adjunct |
| instructor of a minor university |
+------------------------------------+
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------------------------------
Date: Sat, 12 May 2001 13:11:19 -0400 (EDT)
From: Jason Stratos Papadopoulos <[EMAIL PROTECTED]>
Subject: Mersenne: stopping Win98 from needlessly swapping
Hey everybody. I recently replaced my regular GIMPS machine with a 1GHz K7
system carrying 256MB of virtual channel SDRAM. The machine is crunching
through the last of the double checking assignments its predecessor was
issued, and I noticed that the per-iteration time of .075 seconds is a
little worse than the 1GHz Athlon reference system on the GIMPS homepage
(.07 seconds). I would have thought that the extra bandwidth VCSDRAM
provided would have helped things (sorry, no benchmarks using regular
SDRAM yet). Any ideas what could be slowing things down? Taskinfo 2000
shows no unusual processes on the system (the machine runs a PC firewall
in the background, but that uses <1% CPU).
I also noticed that the hard drive light blinks every second or so. Does
win98 agressively swap to disk like windows NT does, even when it's not
needed? At least for NT there was a magic registry hack to make it stop,
which I don't see in '98. I'm wondering if this is the cause of the
slowdown, though with an ATA hard drive the CPU usage should be
minimal. Is there any way short of disabling virtual memory to make the
constant swapping in '98 stop?
Thanks in advance,
jasonp
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Date: Sat, 12 May 2001 14:08:21 -0400
From: Jud McCranie <[EMAIL PROTECTED]>
Subject: Mersenne: Re: 26 exponents
At 01:49 PM 5/12/2001 -0400, George Woltman wrote:
There were 37 on April 15 and 59 on March 11. With a little patience we will
>get there.
OK. My 300 MHz P-II has been doing double checks for months and it does
one of that size in about 20 days or so. Since only 9 have been finished
in the last 28 days either the remainder are running on much slower
machines than mine, or they have been abandoned.
>The "makes the most sense" assignments are based strictly on CPU speed.
>My theory is that the average user with a slowish machine would rather
>complete one double-check in a month or two rather than wait 4 times as
>long for a first time check.
That's true. My last first-time check took 3 months, which is why I went
to double checking, which take about 3 weeks.
...All 4 results will be returned in 44 days.
Great!
+------------------------------------+
| Jud McCranie |
| |
| former temporary part-time adjunct |
| instructor of a minor university |
+------------------------------------+
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Date: Sat, 12 May 2001 14:20:36 -0400
From: Jud McCranie <[EMAIL PROTECTED]>
Subject: Mersenne: Re: 26 exponents
At 01:49 PM 5/12/2001 -0400, George Woltman wrote:
In my last email, I alluded to how the server has some strange behavior when
>the double-checking and first-time testing ranges overlap. One such glitch is
>that if one of these 26 exponents expires, it is reassigned as a double-check
>(and will have to wait until all lower exponents are assigned).
A thought (but it would mean more work) is that if an exponent expires, it
gets reassigned to someone who has completed at least one exponent, to keep
the progress going. These unfinished exponents in the 6,000,000 range were
originally assigned so long ago that they must have been dropped several times.
+------------------------------------+
| Jud McCranie |
| |
| former temporary part-time adjunct |
| instructor of a minor university |
+------------------------------------+
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Date: Sat, 12 May 2001 11:40:56 -0700
From: "John R Pierce" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: stopping Win98 from needlessly swapping
> I also noticed that the hard drive light blinks every second or so. Does
> win98 agressively swap to disk like windows NT does, even when it's not
> needed? At least for NT there was a magic registry hack to make it stop,
> which I don't see in '98. I'm wondering if this is the cause of the
> slowdown, though with an ATA hard drive the CPU usage should be
> minimal. Is there any way short of disabling virtual memory to make the
> constant swapping in '98 stop?
thats probably just CDROM polling to check for autoinsert. not enough
overhead to sweat (probably something like 0.1%)
- -jrp
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Date: Sat, 12 May 2001 15:26:21 -0400
From: Nathan Russell <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Re: 26 exponents
On Sat, 12 May 2001 14:20:36 -0400, Jud McCranie wrote:
>At 01:49 PM 5/12/2001 -0400, George Woltman wrote:
>
>In my last email, I alluded to how the server has some strange behavior when
>>the double-checking and first-time testing ranges overlap. One such glitch is
>>that if one of these 26 exponents expires, it is reassigned as a double-check
>>(and will have to wait until all lower exponents are assigned).
>
>
>A thought (but it would mean more work) is that if an exponent expires, it
>gets reassigned to someone who has completed at least one exponent, to keep
>the progress going. These unfinished exponents in the 6,000,000 range were
>originally assigned so long ago that they must have been dropped several times.
I think that's more of a 'quick fix', and might make new participants
feel that GIMPS doesn't trust them.
It's certainly an interesting topic for discussion, though.
Nathan
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Date: Sat, 12 May 2001 16:04:17 -0400
From: Jud McCranie <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Re: 26 exponents
At 03:26 PM 5/12/2001 -0400, Nathan Russell wrote:
I think that's more of a 'quick fix', and might make new participants
>feel that GIMPS doesn't trust them.
Yes, but a new user need not know that they don't get an exponent that has
expired until they have finished an assignment. My point is that if an
exponent is dropped, it could be reassigned to someone that has shown a
willingness to finish it.
I've been steadily working on GIMPS for nearly 5 years, always 1 fulltime
machine, occasionally 2. I've been doing doublechecks in the 6,000,000
range for a few months because I use a 300 MHz machine. I know
doublechecking is important. But then I see these few gaps under M38? and
I think "I could have done several of those." I know there are going to be
a lot of people who start GIMPS and drop it, and I know that that the gaps
will eventually be filled in.
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Date: Sat, 12 May 2001 20:14:18 -0000
From: "Brian J. Beesley" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: missing exponents?
On 12 May 2001, at 10:22, George Woltman wrote:
> I did this yesterday. Not all exponents are triple checks, some were exponents
> that were never added to the servers list of exponents to double-check.
It so happens I grabbed 7 DC assignments around 4.9 million this
morning. In George's hrf3 database file (the version dated May 6th),
two of them have one entry, two have two entries and three have three
entries. Obviously this is a small sample, but this appears to
suggest a high rate of submission of results with mismatching
residuals. In the case of each of the three exponents with three
completed LL tests, one of these was done using an old version which
did not support offset whilst the other two were done with versions
which do support variable offset. The chance of offsets matching
(thus making the double check invalid even if the residuals match) is
rather small, so the reason a third or fourth run is neccessary is
very probably because results with mismatching residuals are being
submitted for some reason. Most probably random glitches?
>
> To make matters worse, Primenet was not originally designed to
> hand out double-checking assignments. This has resulted in some minor
> glitches, especially when double-checking and first-time checking ranges
> overlap.
>
> Scott/Entropia gave me a simple tool to do some remote server database
> maintenance. I can schedule triple-checks by essentially telling the server
> to forget about the double-check result it already has.
Presumably what happens is as follows:
(a) if a _first_ test result is submitted in this range, PrimeNet
"chalks it up" as a "cleared exponent"; then George recycles the
exponent for double-checking, and it loses its "cleared" status;
(b) when a DC assignment completes, again PrimeNet marks the exponent
as "cleared"; if it turns out that the residuals don't match, or (on
the odd occasion) the double check is invalid because the offsets
match, the exponent has to be recycled and again the "cleared" status
count drops.
>
> This is not a setback for the project. To get accurate counts of the master
> database, visit http://www.mersenne.org/status.htm. There you will see
> that 157,484 exponents have been double-checked and 127,720 exponents
> have been tested once.
Yes, I fail to see how _any_ completed assignment can possibly set
the project back!
Regards
Brian Beesley
1775*2^332181+1 is prime! (100000 digits) Discovered 22-Apr-2001
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Date: Sat, 12 May 2001 16:38:47 -0400
From: Jud McCranie <[EMAIL PROTECTED]>
Subject: Re: Mersenne: missing exponents?
At 08:14 PM 5/12/2001 +0000, Brian J. Beesley wrote:
rather small, so the reason a third or fourth run is neccessary is
>very probably because results with mismatching residuals are being
>submitted for some reason. Most probably random glitches?
Another nice thing would be if people who have submitted several results
that don't match other people's results they could be notified that they
may have a hardware problem.
+------------------------------------+
| Jud McCranie |
| |
| former temporary part-time adjunct |
| instructor of a minor university |
+------------------------------------+
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Date: Sat, 12 May 2001 20:44:28 -0000
From: "Brian J. Beesley" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Re: 26 exponents
On 12 May 2001, at 15:26, Nathan Russell wrote:
> On Sat, 12 May 2001 14:20:36 -0400, Jud McCranie wrote:
> >A thought (but it would mean more work) is that if an exponent expires, it
> >gets reassigned to someone who has completed at least one exponent, to keep
> >the progress going. These unfinished exponents in the 6,000,000 range were
> >originally assigned so long ago that they must have been dropped several times.
>
> I think that's more of a 'quick fix', and might make new participants
> feel that GIMPS doesn't trust them.
>
> It's certainly an interesting topic for discussion, though.
I don't like the idea, for the reason Nathan indicates - it smacks of
"elitism".
A better "fix" would be to patch PrimeNet so that it can assign an
exponent for two LL test runs simultaneously. (Whichever finishes
first becomes the "LL test", the other is the double-check).
Another useful enhancement for PrimeNet would be to do the job that
George did yesterday automatically each time George releases a new
database (about weekly). Exponents which need first LL tests are
those listed in the hrf4 database file, less those with current or
recently-completed assignments. Exponents which need double-checks
are those listed in the hrf3 database file, up to a certain limit,
again less those with current or recently-completed assignments.
"Recently completed" means since George last used results submitted
via PrimeNet to update his master copy of the database.
PrimeNet could be instructed to ignore exponents in particular ranges
for e.g. manual assignment if neccessary.
If this were implemented, George would have less "routine" work to
do, but he'd still be in control of what was going on by "massaging"
the database files manually on the (hopefully fairly rare) occasions
that intervention was needed.
Regards
Brian Beesley
1775*2^332181+1 is prime! (100000 digits) Discovered 22-Apr-2001
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Date: Sat, 12 May 2001 17:29:41 EDT
From: [EMAIL PROTECTED]
Subject: Mersenne: games one can play with genuine composites
I'm catching up on sveral months' worth of digests, so some of
this has been covered by others.
On 23 April 2001, Brian J. Beesley wrote:
> AFAIK the largest number currently known to be composite but with no
> known factors is 2^33219281-1, the only 10 million digit Mersenne
> number which has been LL tested twice with matching final residual.
> (Rick Pali, 2000 & Brian Beesley, 2001) This number has been trial
> factored up to 2^68 and subjected to P-1 with B1=495000.
Ah, but if C is composite with no known factors, so is 2^C - 1.
Or, to paraphrase the famous poem about the wee beasties:
People brag about huge composites C,
And hope none larger will smite 'em,
But then 2^C - 1 is composite, too,
And so on, ad infinitum.
Hans Riesel made the same point in his reply of 26 Apr 2001, to which
Brian replied:
> It is certainly true that, for composite c, 2^c-1 is composite. It
> does _not_ follow that no factors of 2^c-1 are known - even if c is
> itself a Mersenne number.
OK, so what factors of 2^C - 1 are known, for C = 2^33219281-1 ?
Now it is possible that for C composite and f the smallest factor
of C (known or not), 2^C - 1 may in fact have a smaller factor than
2^f - 1 (more on this below), but for C sufficiently large, it will
nearly always be more difficult to find a factor of 2^C - 1 than of C,
if for no other reason that arithmetic modulo C will be much cheaper
than arithmetic modulo the much larger 2^C - 1.
Please don't think that I'm picking on Brian - Crandall, Papadopoulos
and I made similar claims about F24 being the largest genuine composite
at the time we completed our machine proof of that number, and were
similarly put in our place by one of the reviewers of the resulting
manuscript.
On 28 Apr 2001, Peter Montgomery wrote:
> Show us how the factors
>
> 131009 of M_(M11) = 2^(2^11 - 1) - 1
> 724639 of M_(M11)
> 285212639 of M_(M23)
>
> lead to factorizations of M11 and M23.
As Peter well knows, if C = a.b, then (2^a - 1) and (2^b - 1)
are factors of (2^C - 1), but there will generally be other factors
of (2^C - 1), too. The above are examples of these "other factors"
and as such don't help us find factors of 2^11 - 1. But the factor
8388607 = (2^23 - 1) of M_(M11) does lead to a factor of M11, as does
618970019642690137449562111 = (2^89 - 1).
Of course if C has no small factors, finding factors of the special
form (2^a - 1) will be much more difficult (in general) than finding
smaller factors not of this special form, thus attempting to factor
2^C - 1 in order to factor C would seem rather foolish.
- -Ernst
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Date: Sat, 12 May 2001 17:55:05 -0400
From: Jud McCranie <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Re: 26 exponents
At 08:44 PM 5/12/2001 +0000, Brian J. Beesley wrote:
I don't like the idea, for the reason Nathan indicates - it smacks of
>"elitism".
>
>A better "fix" would be to patch PrimeNet so that it can assign an
>exponent for two LL test runs simultaneously. (Whichever finishes
>first becomes the "LL test", the other is the double-check).
But that also seems elitist. If you've got a 1.0 GHz system and the other
person has a 1.2GHz system, you're relegated to the double check because
your system is a little slower. The other way the "elite" would be the
ones who have completed at least 1 exponent. I think of that more as
"productive" or "reliable" than elite.
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Date: Sat, 12 May 2001 18:21:17 -0400
From: Jud McCranie <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Re: 26 exponents
>I don't like the idea, for the reason Nathan indicates - it smacks of
>>"elitism".
By my idea, new users would get untested exponents - they just wouldn't get
one that had already been abandoned.
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Date: Sat, 12 May 2001 21:02:04 -0400
From: George Woltman <[EMAIL PROTECTED]>
Subject: Mersenne: Pentium 4 owners - pre-beta prime95 release available
Hi,
The P4-optimized version of prime95 is ready for adventurous users
to try out. Ordinarily I would not release a trial version at this point,
but I'm sure
P4 owners are itching for a 3x performance boost.
If you do not own a P4, then DO NOT DOWNLOAD THIS VERSION.
It contains no new features and your results will be marked invalid if we
later discover a bug in this code.
ECM does not work, P-1 factoring and LL testing appear to be
operational.
If you try out this version, please let me know of any problems. It would
be helpful if you ran double-check assignments for a few weeks. Also, please
send me some benchmarks to add to http://www.mersenne.org/bench.htm
Mine are already there.
The new version can be downloaded at
ftp://mersenne.org/gimps/p95v21a.zip This is the only link to this
version - you won't find a link on the web site.
Have fun,
George
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Date: Sat, 12 May 2001 21:39:30 -0400
From: Nathan Russell <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Re: 26 exponents
On Sat, 12 May 2001 18:21:17 -0400, Jud McCranie wrote:
>
>>I don't like the idea, for the reason Nathan indicates - it smacks of
>>>"elitism".
>
>By my idea, new users would get untested exponents - they just wouldn't get
>one that had already been abandoned.
There would still be a distinction drawn between 'new' and
'experienced' users, and I think drawing any such distinction would
make new users feel less valued - and quite possibly lead them to join
one of the other fairly large projects, all of which are completely,
or nearly completely, automated.
Nathan
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Date: Sun, 13 May 2001 07:51:21 -0000
From: "Brian J. Beesley" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: games one can play with genuine composites
On 12 May 2001, at 17:29, [EMAIL PROTECTED] wrote:
> Ah, but if C is composite with no known factors, so is 2^C - 1.
... and 2^(2^C-1)-1, and 2^(2^(2^C-1)-1)-1, ...
So there _isn't_ a "largest", unless you disallow this construct.
providing, of course, that there is at least one such C. Actually
there is an adequate and increasing supply of such C's - namely those
values of 2^p-1 (for _prime_ p) which have been doublechecked by
GIMPS/Primenet but which have no known factors. This situation is
likely to persist unless someone can find a foolproof means of
factorizing prime-exponent Mersenne numbers which executes at least
as fast as the Lucas-Lehmer test. (Now there's a challenge!)
> Or, to paraphrase the famous poem about the wee beasties:
>
> People brag about huge composites C,
> And hope none larger will smite 'em,
> But then 2^C - 1 is composite, too,
> And so on, ad infinitum.
Precisely - providing ... (see above)
>
> Hans Riesel made the same point in his reply of 26 Apr 2001, to which
> Brian replied:
>
> > It is certainly true that, for composite c, 2^c-1 is composite. It
> > does _not_ follow that no factors of 2^c-1 are known - even if c is
> > itself a Mersenne number.
>
> OK, so what factors of 2^C - 1 are known, for C = 2^33219281-1 ?
AFAIK, none.
> Now it is possible that for C composite and f the smallest factor
> of C (known or not), 2^C - 1 may in fact have a smaller factor than
> 2^f - 1 (more on this below), but for C sufficiently large, it will
> nearly always be more difficult to find a factor of 2^C - 1 than of C,
> if for no other reason that arithmetic modulo C will be much cheaper
> than arithmetic modulo the much larger 2^C - 1.
Well - it's certainly feasible to look for factors of (for example)
2^(2^727-1)-1 using the mmfac program, & with luck a factor with a
reasonably small k might be found. AFAIK not a great deal of effort
has been expended. A great deal of effort _has_ gone into looking for
a factor of 2^727-1 without success, & we're now pretty sure that the
smallest factor is bigger than 10^50.
The point is that, unless someone can demonstrate that there is a
procedure for determining a factor of M(C) given a factor of M(M(C)),
it is at least possible (maybe very unlikely, but _possible_) that
there might be, now or at some future time, at least one number C
such that a factor of M(M(C)) is known whilst there is no known
factor of M(C).
A rigorous demonstration of how to determine a factor of M(C) given
any factor of M(M(C)) would be sufficient to demolish me, but
meantime I stand by my statement.
If someone could merely demonstrate that, if the smallest factor of
c = 2^p-1 is 2kp+1 for some k, C = 2^c-1 and the smallest factor of
C with the form 2Kc+1 is 2Kc+1 for some K, then K > k^x for some
x > 0, this would show that searching for factors of C without
knowledge of factors of c is probably _unlikely_ to be successful.
But, even though this demonstration would be an advance in the
mathematical sense, it would not prove the theoretical impossibility
of finding a factor of C without knowing any factor of c.
If the limit x could be raised to 1, then any systematic search for
factors of C without knowledge of factors of c would be proved to be
ridiculously wasteful of computing time, but again without proving
that it couldn't possibly be successful, if tried.
>
> Please don't think that I'm picking on Brian
Oh, I don't! It's important to be precise about claims like this!
I'm reminded of the story of three scientists travelling by train
from London to Edinburgh. As the train crosses the border into
Scotland, they observe a black sheep in an otherwise empty field.
Astrophysicist: "So, all Scottish sheep are black!"
Physicist: "No, at least some Scottish sheep are black!"
Mathematician (after long pause): "No, in Scotland there exists at
least one sheep, at least one side of which appears to be black."
Regards
Brian Beesley
1775*2^332181+1 is prime! (100000 digits) Discovered 22-Apr-2001
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End of Mersenne Digest V1 #849
******************************
