Mersenne Digest Wednesday, July 7 1999 Volume 01 : Number 594
----------------------------------------------------------------------
Date: Mon, 05 Jul 1999 18:50:31 -0700
From: Eric Hahn <[EMAIL PROTECTED]>
Subject: Mersenne: IPS Factoring Assignments
I was just about going to ask if George was going to
more factoring assignments available to IPS or if
IPS just wasn't showing ones that had been made
availabe, when I noticed that the range of
10.0 - 10.2 Mil was posted.
Now instead of having enough for about 2 weeks,
there are enough for about 7 weeks, since GIMPS
members go through them at a rate of ~1000 per week
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Date: Mon, 05 Jul 1999 21:50:42 -0700
From: Eric Hahn <[EMAIL PROTECTED]>
Subject: Mersenne: M38 = M6972593
>(Note to Scott - create a dummy non-zero residue a stick it
>in the cleared exponents report).
Too late!! The Cleared Exponents Report reads:
6972593 62 P 0x0000000000000000 01-Jun-99 13:57 nayan precision-mm
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Date: Tue, 6 Jul 1999 10:47:35 +0200 (MET DST)
From: "Benny.VanHoudt" <[EMAIL PROTECTED]>
Subject: Mersenne: question
Hi,
I wonder if any one can help me on the following:
First consider the set of all mersenne numbers 2^n - 1,
then we know that an infinite number of these are NOT prime,
e.g., the set 2^n - 1 with n itself NOT prime.
Now lets only focus on the set 2^p - 1 with p prime, i.e., the set
of numbers that we are checking out at GIMPS. Has anyone proven that
an infinite number these are NOT prime (this is VERY likely to be
true)? If so, how can one prove this easily (it is probably not
possible to indentify a subset that is NOT prime as above
because then we would not consider all of them for GIMPS)?
Thanks,
Benny
- -------------------------------------------------------------------
Benny Van Houdt,
University of Antwerp
Dept. Math. and Computer Science
PATS - Performance Analysis of Telecommunication
Systems Research Group
Universiteitsplein, 1
B-2610 Antwerp
Belgium
email: [EMAIL PROTECTED]
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Date: Tue, 6 Jul 1999 09:52:59 -0400 (EDT)
From: Lucas Wiman <[EMAIL PROTECTED]>
Subject: Re: Mersenne: question
> Now lets only focus on the set 2^p - 1 with p prime, i.e., the set
> of numbers that we are checking out at GIMPS. Has anyone proven that
> an infinite number these are NOT prime (this is VERY likely to be
> true)?
It's nice to be able to say this, but it is in the FAQ. Check it out
at http://www.tasam.com/~lrwiman/FAQ-mers
The last three questions (those in section 4) are pertinate to these questions.
I would ask that before anyone sends a question to the list, please check
the FAQ if it deals with basic questions involving the following:
(1) Basics of a mersenne number (what is it, how many digits, etc...)
(2) The Lucas-Lehmer test (repeating LL remainders, modular arithmetic, etc...)
(3) Factoring Mersenne numbers (how is it done, how do we sieve, etc...
(4) Distribution of Mersenne primes and numbers (how many mersenne primes,
and how factors and mersenne primes are distributed)
If you still have questions after reading the relevant sections of the
FAQ, by all means send them to the list!!
Thank you,
Lucas Wiman
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Date: Tue, 6 Jul 1999 16:30:23 +0200
From: "Steinar H. Gunderson" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: M38 = M6972593
On Mon, Jul 05, 1999 at 09:50:42PM -0700, Eric Hahn wrote:
>>(Note to Scott - create a dummy non-zero residue a stick it
>>in the cleared exponents report).
>Too late!! The Cleared Exponents Report reads:
I think he meant `next time' :-)
/* Steinar */
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Date: Tue, 06 Jul 1999 11:22:26 -0400
From: Jud McCranie <[EMAIL PROTECTED]>
Subject: Re: Mersenne: question
At 10:47 AM 7/6/99 +0200, Benny.VanHoudt wrote:
>Now lets only focus on the set 2^p - 1 with p prime, i.e., the set
>of numbers that we are checking out at GIMPS. Has anyone proven that
>an infinite number these are NOT prime (this is VERY likely to be
>true)? If so, how can one prove this easily (it is probably not
>possible to indentify a subset that is NOT prime as above
>because then we would not consider all of them for GIMPS)?
>
If 2p+1 is prime then it divides 2^p-1. If it has been proven that there are
in infinite number of prime pairs p and 2p+1 then this proves that there are an
infinite number of 2^p-1 that is not prime when p is prime. These are called
Sophie Germain primes, and it has been proven that there are an infinite number
of them, therefore there are an infinite number of composites of the form 2^p-1
when p is prime.
+----------------------------------------------+
| Jud "program first and think later" McCranie |
+----------------------------------------------+
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Date: Tue, 06 Jul 1999 11:35:58 -0400
From: Jeff Woods <[EMAIL PROTECTED]>
Subject: Re: Mersenne: M38 = M6972593
NOW it does, after the official announcement.... Remember when Roland
found M37? Someone found a 0x000000000000000 residue in the report and
beat George to the punch, so Scott modified the reports so that they would
NOT post a zero residue automatically. So THIS time, when word came that
we'd found a potential prime, some enterprising person immediately grabbed
the "assigned exponents" file, and the "cleared exponents" file, and by the
process of elimination, deduced the prime number because it was the ONLY
candidate listed as "assigned" but was not EITHER cleared as non-prime or
still in progress.
George was telling Scott to correct for this 'leak' so that a really
determined person could not do a comparison-elimination to deduce a prime
number find before George announces it.
Of course, Curt Noll's web page made that a pointless exercise... ;-)
At 09:50 PM 7/5/99 -0700, you wrote:
> >(Note to Scott - create a dummy non-zero residue a stick it
> >in the cleared exponents report).
>
>Too late!! The Cleared Exponents Report reads:
>
>6972593 62 P 0x0000000000000000 01-Jun-99 13:57 nayan precision-mm
>
>
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Date: Tue, 6 Jul 1999 13:05:27 -0400 (EDT)
From: Lucas Wiman <[EMAIL PROTECTED]>
Subject: Re: Mersenne: question
>If 2p+1 is prime then it divides 2^p-1. If it has been proven that there are
>in infinite number of prime pairs p and 2p+1 then this proves that there are
>an infinite number of 2^p-1 that is not prime when p is prime. These are
>called Sophie Germain primes, and it has been proven that there are an
>infinite number of them, therefore there are an infinite number of composites
>of the form 2^p-1 when p is prime.
This is not quite right. The primes must be ==3 mod 4. For example,
29 is prime and ==1 mod 4, but 59 does not divide 2^29-1.
I'm not sure whether or not it has been proven whether or not there are
an infinity of Sophie Germain primes of the form 4*n+3. I imagine there
would be, as there are an infinity of primes in the form 4*n+1 and 4*n+3.
- -Lucas Wiman
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Date: Tue, 6 Jul 1999 19:16:58 +0200 (MET DST)
From: [EMAIL PROTECTED]
Subject: Re: Mersenne: question
Jud McCranie <[EMAIL PROTECTED]> writes:
> At 10:47 AM 7/6/99 +0200, Benny.VanHoudt wrote:
> >Now lets only focus on the set 2^p - 1 with p prime, i.e., the set
> >of numbers that we are checking out at GIMPS. Has anyone proven that
> >an infinite number these are NOT prime (this is VERY likely to be
> >true)? If so, how can one prove this easily (it is probably not
> >possible to indentify a subset that is NOT prime as above
^
> >because then we would not consider all of them for GIMPS)?
> >
> If 2p+1 is prime then it divides 2^p-1. If it has been proven that there are
> in infinite number of prime pairs p and 2p+1 then this proves that there are an
> infinite number of 2^p-1 that is not prime when p is prime. These are called
> Sophie Germain primes, and it has been proven that there are an infinite number
> of them, therefore there are an infinite number of composites of the form 2^p-1
> when p is prime.
Please leave adequate white space in your right margin.
Benny's twice-indented (indentified?) text twice still reads well, but
three of Jud's indented lines wrap around on my 80-character screen.
It is _conjectured_ that p and 2p+1 are simultaneously
prime infinitely often, but I have seen no proof.
This is related to the twin prime conjecture, in which p and p+2
are simultaneously prime. More generally, if f1(x) and f2(x) are
irreducible polynomials with integer coefficients such that
i) f1(x) and f2(x) approach +infinity as x -> +infinity
[This excludes constant polynomials, and 3 - 7*x.];
ii) For each prime q there exists an integer n such that
q does not divide the product f1(n)*f2(n)
[This excludes f1(x) = x and f2(x) = x + 1.];
then the conjecture predicts infinitely many integers n
for which f1(n) and f2(n) are simultaneously prime.
A variation of this conjecture extends the result to more
than two polynomials. Even the one-polynomial result
is unproven when its degree exceeds 1: are there
infinitely many primes of the form x^2 + 1?
Peter Montgomery
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Date: Tue, 6 Jul 1999 18:55:12 +0100
From: "Brian J. Beesley" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: question
On 6 Jul 99, at 11:22, Jud McCranie wrote:
> If 2p+1 is prime then it divides 2^p-1.
Only if p (and therefore 2p+1 also) are congruent to 3 (modulo 4).
> If it has been proven that there are
> in infinite number of prime pairs p and 2p+1 then this proves that there are an
> infinite number of 2^p-1 that is not prime when p is prime.
True...
> These are called
> Sophie Germain primes, and it has been proven that there are an infinite number
> of them,
Can you please supply a reference to this proof? Chris Caldwell's
Prime Pages show this as a conjecture (with a strong heuristic
argument).
See http://www.utm.edu/research/primes/lists/top20/SophieGermain.html
In any case, proving that there an infinite number of S-G primes
congruent to 3 (modulo 4) is, presumably, a bit harder - though it
would seem very likely to be true - possibly a bit _less_ likely than
there being only a finite number of composite Mersenne numbers with
prime exponents, though!
Regards
Brian Beesley
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Date: Tue, 06 Jul 1999 14:55:54 -0400
From: Jud McCranie <[EMAIL PROTECTED]>
Subject: Re: Mersenne: question
At 06:55 PM 7/6/99 +0100, Brian J. Beesley wrote:
>
>Can you please supply a reference to this proof? Chris Caldwell's
>Prime Pages show this as a conjecture (with a strong heuristic
>argument).
No, I was wrong about it having been proven.
+----------------------------------------------+
| Jud "program first and think later" McCranie |
+----------------------------------------------+
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Date: Tue, 06 Jul 1999 14:53:56 -0400
From: Jud McCranie <[EMAIL PROTECTED]>
Subject: Re: Mersenne: question
At 01:05 PM 7/6/99 -0400, Lucas Wiman wrote:
>I'm not sure whether or not it has been proven whether or not there are
>an infinity of Sophie Germain primes of the form 4*n+3.
Whoops - it hasn't been proven.
+----------------------------------------------+
| Jud "program first and think later" McCranie |
+----------------------------------------------+
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Date: Tue, 06 Jul 1999 14:57:38 -0400
From: Jud McCranie <[EMAIL PROTECTED]>
Subject: Re: Mersenne: question
At 07:16 PM 7/6/99 +0200, [EMAIL PROTECTED] wrote:
> Please leave adequate white space in your right margin.
>Benny's twice-indented (indentified?) text twice still reads well, but
>three of Jud's indented lines wrap around on my 80-character screen.
I think I have mine set to wrap at 60 characters.
>
> It is _conjectured_ that p and 2p+1 are simultaneously
>prime infinitely often, but I have seen no proof.
That's right. I was wrong about it being proven.
+----------------------------------------------+
| Jud "program first and think later" McCranie |
+----------------------------------------------+
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Date: Wed, 7 Jul 1999 00:37:43 +0200
From: "Steinar H. Gunderson" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: LL & Factoring DE Crediting
On Tue, Jun 29, 1999 at 12:12:28PM +0200 (OK, late reply, it suddenly
struck me that I hadn't replied...), Sturle Sunde wrote:
>number which is tested already, you climb by pushing someone else down.
That isn't very likely to happen, is it? Am I the only one who doesn't
trial-factor random LL tested exponents? :-)
>If I don't factor far enough, that will eventualy happen to me.
Hmmmm, perhaps...
(Of course, factoring is a good idea in general; it saves you from
wasting times on LL tests.)
>Therefore I think that Georges
>formula, just counting LL-results for every Mersenne without a factor
>in the database and give credit to the people who tested those numbers,
>is a beautiful solution.
But what if a person had a load (say any number for the discussion, 1000
might be a bit extreme, but still _possible_) of 486s only, and didn't
want them to LL test becuase that takes _ages_? (As we've discussed
earlier, some Dells have problems with flickering during LL tests, which
I've experienced myself the last two weeks.)
(Then again, it saves some problems -- people with P6-class CPUs (that have
almost twice as much `factoring speed' as `LL speed' per cycle
(in P90 CPU year)) won't be tempted to do factoring only, and run up
the ranks :-))
As long as you do get assigned normal, first-time LL tests (double-checks
are already trial-factored with only a marginal chance of a factor missed,
so you get an unfair advantage -- no factoring has to be done), George's
setup is perfect. When things get a bit more complex, IPS is better, IMHO.
/* Steinar */
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Date: Tue, 6 Jul 1999 19:26:04 EDT
From: [EMAIL PROTECTED]
Subject: Mersenne: Spreading the Word
Well, I've fully updated my GIMPS/PrimeNet banners page. I don't know if
anyone but Mr. Kurowski uses them (which is really great of him!), but it's
worth a shot. As usual, they're up-to-date for the time being. Those
statistics do change fast. They are all 40x400 pixels, 256 color .GIF format.
Despite the sluggishness of the gallery page, each individual banner loads
quickly. I have 36 versions in total. GIMPS8.GIF in particular looks nifty.
If you have a web page, *please* use them somewhere so GIMPS gets more
members! There's even a little one (at the bottom of the gallery page) that
just says 2^P - 1.
For those interested:
The gallery page can be found at http://mersenne.cjb.net/
The FTP directory of the banners is at ftp://members.aol.com/stl137/bannerz/
There is now a .ZIP file of all the banners on the gallery page.
S.T.L.
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Date: Tue, 06 Jul 1999 18:18:05 -0700
From: Eric Hahn <[EMAIL PROTECTED]>
Subject: Mersenne: SJ Mercury News
For those of you who are interested, the San Jose
Mercury News has published the story.
http://www.mercurycenter.com/premium/scitech/docs/prime06.htm
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Date: Tue, 06 Jul 1999 21:37:12 -0700
From: Spike Jones <[EMAIL PROTECTED]>
Subject: Re: Mersenne: SJ Mercury News
> Eric Hahn wrote: For those of you who are interested, the San Jose
> Mercury News has published the story.
>
> http://www.mercurycenter.com/premium/scitech/docs/prime06.htm
Yes, they did but I was disappointed in the article. No mention of
the GIMPS site! {8-[ All those SETI plugs! {8-| Lets wait and see if
our numbers go up in six weeks or so. spike
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Date: Wed, 7 Jul 1999 09:58:03 +0200 (MET DST)
From: "Benny.VanHoudt" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: question
Hi,
Brian Beesley wrote:
>
> If p, 2p+1 are both prime and p = 4k+3 for some integer k then 2p+1
> is a factor of 2^p-1. Therefore, if there is an infinite supply of
> Sophie Germain primes congruent to 3 (modulo 4), there is an infinite
> supply of compound Mersenne numbers with prime exponents.
>
> However, there seems to be no proof that there is an infinite supply
> of Sophie Germain primes, let alone of the subclass of S-G primes
> congruent to 3 (mod 4). There is a strong heuristic argument that
> predicts the number of S-G primes less than any given limit -
> interestingly, the formula contains the "twin primes" constant.
>
> There are other heuristic arguments that there is an infinite number
> of composite Mersenne numbers with prime exponents , e.g. since there
> are an infinite number of primes, and the probability that a
> particular prime generates a prime Mersenne number decreases with the
> size of the prime, the expected total number of composite Mersenne
> numbers with prime exponents is the sum of an infinite series of
> terms, with the terms asymptotically approaching 1. The sum is, of
> course, infinite, "Q.E.D." (But this isn't a formal proof!)
>
> The other way of putting this is that, if there are only a finite
> number of primes which generate a compound Mersenne number, there
> must be a _largest_ prime p such that 2^p-1 is compound, with 2^q-1
> prime for all prime q > p. This state of affairs seems absurd, in
> view of the fact that one would expect the probability that 2^q-1 is
> prime for any particular prime q to be very small as q tends to
> infinity.
>
You are correct when you state that this seems absurd and I agree
that there are surely going to be an infinite number of composite
Mersenne numbers with prime exponents !?
I just wondered whether there is a 'formal' proof of this fact,
and if so where can I find it ?
Benny;
- -------------------------------------------------------------------
Benny Van Houdt,
University of Antwerp
Dept. Math. and Computer Science
PATS - Performance Analysis of Telecommunication
Systems Research Group
Universiteitsplein, 1
B-2610 Antwerp
Belgium
email: [EMAIL PROTECTED]
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Date: Wed, 7 Jul 1999 11:26:35 +0200
From: "Grieken, Paul van" <[EMAIL PROTECTED]>
Subject: Mersenne: results.txt
I have a question about the result file in prime.
My computer automaticly connects the prime server when a calculation is
ready.
Now I saw that the file results.txt still contains the result of a
former calculation.
If the current calculation is ready and the computer reach the server
will the old one also be send to the server?
Is this correct?
Or do I have to delete something from the result.txt file
bye,
Paul van Grieken
Alcatel Telecom Nederland
afd: T-TAC NE Kamer:4121
Postbus 3292
2280GG rijswijk
Nederland
Phone: + 31 70 307 9353
Fax: + 31 70 307 9476
Email: [EMAIL PROTECTED]
Prive:
Ruys de Beerenbrouckstraat 1
2613AS Delft
Netherlands
Marklin collector
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Date: Wed, 07 Jul 1999 12:02:13 +0200
From: "Steinar H. Gunderson" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: results.txt
At 11:26 07.07.99 +0200, Grieken, Paul van wrote:
>If the current calculation is ready and the computer reach the server
>will the old one also be send to the server?
No. When Prime95 has something to send to the server, another file, called
prime.spl, is called. The results.txt file is for manual sending (and for
your own logging purposes) only. (Once upon a time, there was no Primenet,
you know.)
You do not have to delete anything. Everything goes automatically.
/* Steinar */
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Date: Wed, 07 Jul 1999 06:58:42 -0400
From: Peter Doherty <[EMAIL PROTECTED]>
Subject: Re: Mersenne: results.txt
The results file is a history file. If it mentions it did a test on a
number, and found it's not prime, it's already told primnet all that. It
just keeps a history file in there the way a lot of programs do.
- --Peter
At 11:26 07/07/1999 +0200, you wrote:
>I have a question about the result file in prime.
>My computer automaticly connects the prime server when a calculation is
>ready.
>Now I saw that the file results.txt still contains the result of a
>former calculation.
>If the current calculation is ready and the computer reach the server
>will the old one also be send to the server?
>Is this correct?
>Or do I have to delete something from the result.txt file
>bye,
>
>Paul van Grieken
>Alcatel Telecom Nederland
>afd: T-TAC NE Kamer:4121
>Postbus 3292
>2280GG rijswijk
>Nederland
>
>Phone: + 31 70 307 9353
>Fax: + 31 70 307 9476
>Email: [EMAIL PROTECTED]
>
>Prive:
>Ruys de Beerenbrouckstraat 1
>2613AS Delft
>Netherlands
>
>Marklin collector
>
>________________________________________________________________
>Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
>
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Date: Thu, 08 Jul 1999 03:17:01 +0700
From: Warut Roonguthai <[EMAIL PROTECTED]>
Subject: Mersenne: (2^p+1)/3
Is there a known prime factor of (2^6972593+1)/3? Is there any web page
that maintains the list of factors of (2^p+1)/3, where p is a Mersenne
prime exponent? Numbers of this form are related to the new Mersenne
conjecture of Bateman, Selfridge, and Wagstaff.
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Date: Wed, 7 Jul 1999 19:29:54 -0500 (CDT)
From: Conrad Curry <[EMAIL PROTECTED]>
Subject: Re: Mersenne: (2^p+1)/3
On Thu, 8 Jul 1999, Warut Roonguthai wrote:
> Is there a known prime factor of (2^6972593+1)/3? Is there any web page
> that maintains the list of factors of (2^p+1)/3, where p is a Mersenne
> prime exponent? Numbers of this form are related to the new Mersenne
> conjecture of Bateman, Selfridge, and Wagstaff.
I created a table that corrected and updated the table from [1].
It is available from http://orca.st.usm.edu/~cwcurry/NMC.html
(2^p+1)/3 is of unknown character for p = 1048573, 1398269, and
6972593. If anyone has factors of these or other probable primes
of (2^p+1)/3 for p>14480, I would appreciate it if you let me know.
[1] P. T. Bateman, J. L. Selfridge and S. S. Wagstaff Jr., "The
New Mersenne Conjecture," Amer. Math. Monthly, 96 (1989) 125-128.
Also see Chris Caldwell's web page
http://www.utm.edu/research/primes/mersenne.shtml
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Date: Wed, 7 Jul 1999 23:04:46 -0300
From: Fabio Dias <[EMAIL PROTECTED]>
Subject: Mersenne: Repeating LL reminder
I know it's almost impossible to detect a repeating LL reminder, but what a LL
repeating reminder means exactly? Can it tell the number's factored form, or other
thing like that? (I'm including here also composite exponents and Sophie-Germain
exponents, such as 2^4-1,2^6-1, 2^11-1...)
Fabio
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End of Mersenne Digest V1 #594
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