Mersenne Digest        Thursday, June 15 2000        Volume 01 : Number 747




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

Date: Tue, 13 Jun 2000 11:26:24 -0700
From: Stefan Struiker <[EMAIL PROTECTED]>
Subject: Mersenne: Are The M-Monsters Available For Trial Factoring?

TeamG:

Love factoring on a fast machine because turnaround is zippy,
and I actually get a result to crow about every 5 or so attempts.

Factoring assignments are assigned, it seems, by PrimeNet only
by that Mystery Algorithm, which I would dearly love to override,
in order to get a 10,000,000 digit M-candidate to attack.

Anyone know how to do this?  The Manual Testing Form system
was still broken this morning anyway. :-(

Best Wishes,
Stefanovic

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

Date: Wed, 14 Jun 2000 09:49:50 +1200 (NZST)
From: Bill Rea <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Server busy - please try again in a few moments

Siegmar wrote:-

>I try to check in some results but I always get this 
>error message... It says I should try it in a few moments,
>but I get this message now since 4-5 days :( Any idea, 
>how I could check in the results?

I've tried checking out a new exponent and get error 576000. It's
been like this for a couple of days. I've got work to check in
as well. I emailed the address given on the error page but haven't
gotten a reply yet.

Bill Rea, Information Technology Services, University of Canterbury  \_ 
E-Mail b dot rea at its dot canterbury dot ac dot nz                 </   New 
Phone   64-3-364-2331, Fax     64-3-364-2332                        /)  Zealand 
Unix Systems Administrator                                         (/' 

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

Date: Tue, 13 Jun 2000 11:32:59 +0200
From: Lem Novantotto <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Slowdown in iteration speed

On Mon, 12 Jun 2000 22:00:57 -0600, in Mersenne_mailing_list you
wrote:
>I just finished a Lucas Lehmer test on exponent 9822067. My PII 350 was
>doing a iteration every .320 seconds. The next exponent it started was
>103500203. It is now taking .421 seconds per iteration. I have a feeling
>this is due to the fact it is using a different FFT.
Hi!
You're right. See http://www.mersenne.org/bench.htm for details.
- -- 
Bye.
      Lem
- ---------- 'CLOCK is what you make of it' ----------
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------------------------------

Date: Wed, 14 Jun 2000 01:11:57 -0700
From: Will Edgington <[EMAIL PROTECTED]>
Subject: Mersenne: Common practice for P-1 math?

     I was wondering if it was common practice (ie: the norm) for P-1
   to take the product of two or more factors when giving out a found
   factor, if two of more factors are found?

Yes, if both factors are "smooth" enough, they could be found as their
product, rather than individually.  "Smooth" is defined as one less
than the factor having no factors larger than the stage one P-1 bound
plus up to one factor between the stage 1 and stage 2 bounds.

     To clarify, I was curious about how P-1 would indicate more than
   one factor being found.  So, I took M113 and fed it into Prime95
   with the bounds of B1=200, B2=20000.  Prime95 notified me that P-1
   had found a factor in Stage #1, and that the factor was
   9734174361238150513.  This factors out to 3391 * 23279 * 65993 *
   1868569, all of which are known factors of M113.

For example, all the primes factors of 3390, 23278, 65992, and 1868568
are likely smaller than 200.  If not, at most one factor of each
number should be between 200 and 20,000.

Note that there are three factors of 9734174361238150512 that are
larger than 20,000; that doesn't matter.

Because of this possibility of new factors being composite, I
sometimes run a script that checks for composite factors in all my
data and my update scripts check all new factors against smaller
factors for the same exponent (to see if the smaller factor is a
factor of the new factor).

All new factors are also checked to verify that they are actually
factors and whether they are also factors of some smaller Mersenne;
the latter is not uncommon for new factors found by P-1 or ECM for
composite exponent Mersenne numbers, but cannot happen for prime
exponent Mersennes.

                                                Will
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------------------------------

Date: Wed, 14 Jun 2000 01:30:17 -0700
From: Will Edgington <[EMAIL PROTECTED]>
Subject: Mersenne: What Happens Once A Factor Has Been Reported?

   Once a factor has been logged for an M-candidate, either by P-1
   or by "the other" method, what M-happens?  Is a different sort
   of double-checking automatically done?

I've forgotten what GIMPS or PrimeNet do in this regard, but all
Mersenne factors sent to me - and George Woltman and several other
people send all the factors they know about to me at some point - are
verified to be correct by my update scripts.  The actual calculation
is done by a short function in the UNIX bc (basic calculator) command,
which is not exactly speedy (nor slow - it's a very fast algorithm,
that loops over the _bits_ of the Mersenne exponent), but it is
completely independent, code-wise, from all the GIMPS and mers package
programs.

My update scripts also automatically download all the new data from
ftp://mersenne.org/gimps, Paul Leyland's Cunningham Project site,
Dr. Wagstaff's site at Purdue, and a few others, typically once every
week or two.

                                                Will

http://www.garlic.com/~wedgingt/mersenne.html
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------------------------------

Date: Wed, 14 Jun 2000 11:41:40 +0200
From: =?iso-8859-1?Q?Ignacio_Larrosa_Ca=F1estro?= <[EMAIL PROTECTED]>
Subject: Mersenne: RE: Exponent lost

I had assigned

Test=9398971,64

but yet it is not in my personal account report. And it is not assigned to
anybody in the

Assigned Exponents Report 14 Jun 2000 09:02

I hope finish this exponent in two days. Did what happen with it?

Best regards,

Ignacio Larrosa Ca�estro
A Coru�a (Espa�a)
[EMAIL PROTECTED]

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

Date: Wed, 14 Jun 2000 10:31:02 -0000
From: "Brian J. Beesley" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Common practice for P-1 math?

On 12 Jun 00, at 23:20, Eric Hahn wrote:

>   I was wondering if it was common practice (ie: the norm) for
> P-1 to take the product of two or more factors when giving out
> a found factor, if two of more factors are found?

I don't know about "common practice", but P-1 uses GCD to find the 
factor. Consequently this factor may indeed be compound, unless extra 
steps are taken to eliminate this possibility.
> 
>   To clarify, I was curious about how P-1 would indicate more
> than one factor being found.  So, I took M113 and fed it into
> Prime95 with the bounds of B1=200, B2=20000.  Prime95 notified
> me that P-1 had found a factor in Stage #1, and that the factor
> was 9734174361238150513.  This factors out to 3391 * 23279 *
> 65993 * 1868569, all of which are known factors of M113.

True enough.

However, if P-1 finds a factor with P bits, and trial factoring to T 
bits has already been done without finding any factor, then the 
factor found by P-1 _must_ be prime unless P > 2T. (For the purposes 
of Prime95, this situation is _most_ unlikely ever to occur, 
therefore it seems reasonable to avoid the extra complications.)

If P-1 does find a factor which is compound, then running P-1 again 
with smaller limits will eventually recover a smaller factor. These 
extra runs will obviously take less time than the original 
"discovery" run. Also, finding _any_ factor is sufficient to 
eliminate an exponent as a Mersenne prime candidate, so decomposing 
the factor found into its prime constituents is not neccessary if P-1 
is being run purely for this reason.


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

Date: Wed, 14 Jun 2000 04:49:05 -0700
From: Paul Leyland <[EMAIL PROTECTED]>
Subject: RE: Mersenne: Common practice for P-1 math?

> From: Brian J. Beesley [mailto:[EMAIL PROTECTED]]

> If P-1 does find a factor which is compound, then running P-1 again 
> with smaller limits will eventually recover a smaller factor. These 
> extra runs will obviously take less time than the original

Indeed, and with care one can usually choose the bounds so only one more run
is necessary.  Factoring c-1 (where c is the composite factor found) and
judiciously chosing which primes to omit is the method.  This factorization
is extremely easy, because of the way in which c was discovered.   In
practice, discarding the prime factor of c found in stage 2 is all that's
usually needed.  If c was found after stage 1, and so there is no large
prime, discarding half (rounded up if the number is odd) of the powers of 2
usually does the trick.

Of course, all these computations are performed on c, and not the original
integer.

It's a pity that a similar procedure isn't known for ECM, or at least not
known to me.


Paul
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------------------------------

Date: Wed, 14 Jun 2000 15:13:54 -0000
From: "Brian J. Beesley" <[EMAIL PROTECTED]>
Subject: RE: Mersenne: Common practice for P-1 math?

On 14 Jun 00, at 4:49, Paul Leyland wrote:

> It's a pity that a similar procedure isn't known for ECM, or at least not
> known to me.

Isn't the point that ECM finds numerically small factors much more 
easily than it finds numerically large factors? Therefore, if a 
"reasonable" amount of trial factoring has been done, it's very 
unlikely that a previously undiscovered factor will be found 
directly, unless it's prime.

It's even less likely that this will happen provided that sufficient 
runs with smaller B-limits are done before going on to larger B-
limits.

Of course, if we find a prime factor which is less than the cube root 
of the number we're working with, the cofactor (found indirectly by 
dividing the number by the new factor) may still be composite. Using 
ECM, the cofactor may in fact be composite even if the new prime 
factor is a bit bigger than the cube root, for reasons connected with 
the probabilistic way in which ECM works. 

One possible method for dealing with numbers with existing known 
factors is to keep the known factors in a database and, when the GCD 
is found to be greater than 1, dividing the result of the GCD by as 
many of the known factors as possible until the result becomes 1 (in 
which case only already known factors have been found) or no more 
known factors are available (in which case we found a new one). This 
would work equally well for P-1 and ECM.


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

Date: Wed, 14 Jun 2000 18:00:12 +0100
From: Yvan Dutil <[EMAIL PROTECTED]>
Subject: Mersenne: An exemple of courage

A list a very couragous guy.

5362403 D   62   4756266   711.6 -11.8  31.2  15-Apr-00 19:32  04-Jul-98
00:30  tp68spa
5447983 D   62   4948807   697.8 -41.8  18.3  11-Apr-00 21:52  17-Jul-98
20:48  S02147
5633231     62   4915200   648.3 -10.9  15.1  28-Apr-00 17:18  05-Sep-98
08:04  t_taufer       couns_jensen
5681243     62   5570559   642.2 -50.4   9.6  23-Apr-00 06:30  11-Sep-98
11:55  jnsilva
 6055787     62    767679   576.9 114.3  61.3  12-Jun-00 21:13  15-Nov-98
17:32  S03383         C9EF8B1C0
6325021     62   5009382   591.9  82.0  66.0  23-May-00 16:03  31-Oct-98
18:22  babylon5
6380057     62   2254783   570.4 -24.5   3.5  22-Mar-00 03:49  22-Nov-98
05:47  mpfeifer       K6-200
6383239     62   3735551   570.0 -37.0   9.0  10-Apr-00 14:44  22-Nov-98
15:51  gpapa          lukehome
6423091     62   3888236   566.0  79.8  78.8  05-Jun-00 09:32  26-Nov-98
14:40  dlanor         laptop

A taste of teh future with the the prime in the 30 000 000 range.

Yvan Dutil

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

Date: Wed Jun 14 12:47:03 2000
From: [EMAIL PROTECTED]
Subject: Mersenne: PrimeNet manual test forms

Manual testers will be pleased to know that the PrimeNet
manual test forms appear to be working once again.

Thanks, Scott et al.

- -ernst

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

Date: Wed, 14 Jun 2000 09:28:05 -0700
From: Paul Leyland <[EMAIL PROTECTED]>
Subject: RE: Mersenne: Common practice for P-1 math?

> From: Brian J. Beesley [mailto:[EMAIL PROTECTED]]
> On 14 Jun 00, at 4:49, Paul Leyland wrote:
> 
> > It's a pity that a similar procedure isn't known for ECM, 
> or at least not
> > known to me.
> 
> Isn't the point that ECM finds numerically small factors much more 
> easily than it finds numerically large factors? Therefore, if a 
> "reasonable" amount of trial factoring has been done, it's very 
> unlikely that a previously undiscovered factor will be found 
> directly, unless it's prime.

Yes and no.  ECM has behaviour very similar to P-1 and P+1 (which is not too
surprising, as they are all essentially the same algorithm) and does indeed
tend to find small factors easier than large ones.  However, if there are
two small factors, each of which are smooth in the appropriate sense, they
will be found together.

> It's even less likely that this will happen provided that sufficient 
> runs with smaller B-limits are done before going on to larger B-
> limits.

Not always true.  I recently was running ECM with very small limits to pick
up factors in the 6 - 10 digits range (yes, I know ECM isn't the optimal
algorithm for factors this small but my ECM program is available and easy to
use) and found a 39 digit composite factor!   It subsequently turned out to
have four distinct prime factors.

Today I found this number 3756482676803749223044867243823 with ECM and
B1=10,000.  It has two factors, each of 16 digits, which could *not* have
been found by trial division in any reasonable time.


Paul



> 
> Of course, if we find a prime factor which is less than the cube root 
> of the number we're working with, the cofactor (found indirectly by 
> dividing the number by the new factor) may still be composite. Using 
> ECM, the cofactor may in fact be composite even if the new prime 
> factor is a bit bigger than the cube root, for reasons connected with 
> the probabilistic way in which ECM works. 
> 
> One possible method for dealing with numbers with existing known 
> factors is to keep the known factors in a database and, when the GCD 
> is found to be greater than 1, dividing the result of the GCD by as 
> many of the known factors as possible until the result becomes 1 (in 
> which case only already known factors have been found) or no more 
> known factors are available (in which case we found a new one). This 
> would work equally well for P-1 and ECM.
> 
> 
> Regards
> Brian Beesley
> 
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------------------------------

Date: Wed, 14 Jun 2000 16:11:32 -0700
From: Stefan Struiker <[EMAIL PROTECTED]>
Subject: Re: Mersenne: An exemple of courage

I need help in understanding this post!

Thanks And Best Wishes,
Stefanovic

Yvan Dutil wrote:

> A list a very couragous guy.
>
> 5362403 D   62   4756266   711.6 -11.8  31.2  15-Apr-00 19:32  04-Jul-98
> 00:30  tp68spa
> 5447983 D   62   4948807   697.8 -41.8  18.3  11-Apr-00 21:52  17-Jul-98
> 20:48  S02147
> 5633231     62   4915200   648.3 -10.9  15.1  28-Apr-00 17:18  05-Sep-98
> 08:04  t_taufer       couns_jensen
> 5681243     62   5570559   642.2 -50.4   9.6  23-Apr-00 06:30  11-Sep-98
> 11:55  jnsilva
>  6055787     62    767679   576.9 114.3  61.3  12-Jun-00 21:13  15-Nov-98
> 17:32  S03383         C9EF8B1C0
> 6325021     62   5009382   591.9  82.0  66.0  23-May-00 16:03  31-Oct-98
> 18:22  babylon5
> 6380057     62   2254783   570.4 -24.5   3.5  22-Mar-00 03:49  22-Nov-98
> 05:47  mpfeifer       K6-200
> 6383239     62   3735551   570.0 -37.0   9.0  10-Apr-00 14:44  22-Nov-98
> 15:51  gpapa          lukehome
> 6423091     62   3888236   566.0  79.8  78.8  05-Jun-00 09:32  26-Nov-98
> 14:40  dlanor         laptop
>
> A taste of teh future with the the prime in the 30 000 000 range.
>
> Yvan Dutil
>
> _________________________________________________________________
> Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
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------------------------------

Date: Wed, 14 Jun 2000 21:13:35 -0400
From: Shel Michaels <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Primenet server

Hi Benny...

    My system behaved in the same way as yours after I installed "Zone
Alarm", a freeware firewall, on my system.  I had failed to configure the
firewall to allow prime95 through, and had failed to configure it to pop up
a notice of the denied attempt.  So, perhaps you installed a firewall?

Bests,
...Shel Michaels

- ----- Original Message -----
From: "Benny.VanHoudt" <[EMAIL PROTECTED]>

> In the last three weeks prime95 hasn't succeeded in contacting the
> Primenet server. I have changed the UseHTTP=0 line in the prime.ini
> to UseHTTP=1 and restarted the program but it doesn't seem to
> make any difference. Any suggestions ?


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

Date: Wed, 14 Jun 2000 23:52:25 -0400
From: George Woltman <[EMAIL PROTECTED]>
Subject: Mersenne: Entropia.com  IP Change

- --=====================_983214578==_.ALT
Content-Type: text/plain; charset="us-ascii"; format=flowed

Hi all,

         The mersenne.org and entropia.com IP address has changed again.
At Brad's request, I'm letting all of you know so that you can report any
problems to him.  Hopefully there will be none.

Regards,
George

>From: Brad Bernard <[EMAIL PROTECTED]>
>To: "'George Woltman'" <[EMAIL PROTECTED]>
>Subject: IP Change
>Date: Wed, 14 Jun 2000 19:50:03 -0700
>
>Hi George,
>Just to let you know, we have had to change the IP once again due to 
>firewall restrictions. It has changed to 216.120.70.80 but I am still 
>serving the 216.120.55.141 IP so we should not have as many problems as 
>last time.
>
>Can you send an email to the Mersenne list letting folks know?  I would do 
>so but have not yet sent anything to the list and not quite sure how to go 
>about doing so.
>
>Thanks,
>Brad

- --=====================_983214578==_.ALT
Content-Type: text/html; charset="us-ascii"

<html>
Hi all,<br>
<br>
<x-tab>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</x-tab>The
mersenne.org and entropia.com IP address has changed again.<br>
At Brad's request, I'm letting all of you know so that you can report
any<br>
problems to him.&nbsp; Hopefully there will be none.<br>
<br>
Regards,<br>
George<br>
<br>
<blockquote type=cite cite>From: Brad Bernard
&lt;[EMAIL PROTECTED]&gt;<br>
To: &quot;'George Woltman'&quot; &lt;[EMAIL PROTECTED]&gt;<br>
Subject: IP Change<br>
Date: Wed, 14 Jun 2000 19:50:03 -0700<br>
<br>
<font face="arial" size=2 color="#0000FF">Hi George,</font><br>
<font face="arial" size=2 color="#0000FF">Just to let you know, we have
had to change the IP once again due to firewall restrictions. It has
changed to 216.120.70.80 but I am still serving the 216.120.55.141 IP so
we should not have as many problems as last time.</font><br>
&nbsp;<br>
<font face="arial" size=2 color="#0000FF">Can you send an email to the
Mersenne list letting folks know?&nbsp; I would do so but have not yet
sent anything to the list and not quite sure how to go about doing
so.</font><br>
&nbsp;<br>
<font face="arial" size=2 color="#0000FF">Thanks,</font><br>
<font face="arial" size=2 color="#0000FF">Brad</font></blockquote></html>

- --=====================_983214578==_.ALT--

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

Date: Thu, 15 Jun 2000 01:14:26 -0700
From: Paul Leyland <[EMAIL PROTECTED]>
Subject: RE: Mersenne: Common practice for P-1 math?

I wrote:

> > From: Brian J. Beesley [mailto:[EMAIL PROTECTED]]
> 
> > If P-1 does find a factor which is compound, then running P-1 again 
> > with smaller limits will eventually recover a smaller factor. These 
> > extra runs will obviously take less time than the original
> 
> Indeed, and with care one can usually choose the bounds so only one more
run
> is necessary.  Factoring c-1 (where c is the composite factor found) and
> judiciously chosing which primes to omit is the method.  This
factorization
> is extremely easy, because of the way in which c was discovered.   In
> practice, discarding the prime factor of c found in stage 2 is all that's
> usually needed.  If c was found after stage 1, and so there is no large
> prime, discarding half (rounded up if the number is odd) of the powers of
2
> usually does the trick.
> 
> Of course, all these computations are performed on c, and not the original
> integer.
> 
> It's a pity that a similar procedure isn't known for ECM, or at least not
> known to me.

On reflection, this last sentence is silly, and arose only because I hadn't
thought about the matter properly.

As long as the coefficients of the curve and the starting point are
recorded, we can re-run exactly the same computation, with the small primes
curtailed as in the p-1 case, on the same curve and the number c.  It's
because my software doesn't normally output the curve and starting point
used that the idea hadn't occurred to me.


Paul
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------------------------------

Date: Thu, 15 Jun 2000 11:04:16 +0100
From: Yvan Dutil <[EMAIL PROTECTED]>
Subject: Re: Mersenne: An exemple of courage

Stefan Struiker wrote:

> I need help in understanding this post!
>

I reformat the table to make it clearer. The come from
the Primenet list of allocated exponents.  It is a list of guys who
have worked on their exponent for a very long time (>> 1 year).
As I said this a taste of teh things to come with the exponents in
the 30 000 000 range.

By the way, they are still working on it and are expected to finish soon.
Dont consider this as an invitation to poach :)

Yvan dutil



>
> Yvan Dutil wrote:
>
> > A list a very couragous guy.
> >
> > 5362403 D   04-Jul-98   tp68spa
> > 5447983 D   17-Jul-98   S02147
> > 5633231      05-Sep-98  t_taufer       couns_jensen
> > 5681243       11-Sep-98  nsilva
> >  6055787     15-Nov-98  S03383         C9EF8B1C0
> > 6325021      31-Oct-98 babylon5
> > 6380057      22-Nov-98  mpfeifer       K6-200
> > 6383239      22-Nov-98 gpapa          lukehome
> > 6423091      26-Nov-98 dlanor         laptop

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

Date: Thu, 15 Jun 2000 03:25:08 -0700
From: Stefan Struiker <[EMAIL PROTECTED]>
Subject: Mersenne: Funny Thing Happened After I Was Driven To Manual Check-In

To All:

Now that manual check-in is finally working, PrimeNet check-in
seems broken.  I decided to send in factor data manually, which was accepted,
but noticed that the v19/v20 designation in my account report vanished for the
machine in question -- throughout.

Any news or info would be appreciated.  I know another server reconfig
was/is being done.

Best Wishes,
Stefanovic


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

Date: Thu, 15 Jun 2000 17:31:48 +0200
From: Martijn <[EMAIL PROTECTED]>
Subject: Mersenne: Assignment "stolen"

Hello,

I just saw that an exponent I am testing (due in about 
20 days) sudennly was removed from my account report. 
When looking in the cleared exponents list, "my" 
exponent is listed as cleared by milbournea (no 
offence). Should I stop testing this exponent or should 
I still await the final result and return it (i.e. 
making a double-check unnecessary / let it be the 
double check.) 

When returning, will the LL time be credited?

Kind Regards, Martijn

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Date: Thu, 15 Jun 2000 16:54:46 -0400
From: George Woltman <[EMAIL PROTECTED]>
Subject: Mersenne: version 20.6

Hi all,

        I just fixed a crash bug.  If you run ECM or P-1 factoring and at
a later time find a factor with trial factoring, then memory is corrupted
probably resulting in a crash.

        This bug is unlikely to affect you, as the normal order is trial
factoring, then P-1 factoring, then an LL test.  Assuming you reboot
once during the LL test, you will not have a problem when you start
trial factoring the next exponent.

Regards,
George

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