Dear Mersenners:
This being the sesquicentennial of the California gold rush,
I thought a fitting tribute would be to move there, this time
to be nearer the silicon, rather than the gold. I was going to
insert an Au-ful pun here, but couldn't come up with one. Si-gh...
As of 1 july, my left
Whilst keeping memory requirements reasonable, we could build a
second stage sieve to eliminate the primes 19, 23, 29 31 in a
second table of size 392863. Doing this would eliminate about 15% of
the candidates remaining from the first pass, whereas the first pass
eliminates about 64%. Apart
hi again,
From: Jud McCranie [EMAIL PROTECTED]
To: Alan Simpson [EMAIL PROTECTED]
CC: [EMAIL PROTECTED]
Subject: Re: Mersenne: this 3/2 conjecture and a result of Wagstaff
Date: Wed, 23 Jun 1999 10:54:19 -0400
There's no heuristic argument that I know of for 3/2 (it just fits known
data
(Sorry, messed up a key strok and sent my last message before
I was ready.)
For the last day I have received :
ERROR: Primenet error: 12029
Can someone help me with the meaning of this particular
message. I do work behind a proxy server but have never
had a problem using the http
Mersenne DigestThursday, June 24 1999Volume 01 : Number 587
--
Date: Tue, 22 Jun 1999 20:30:09 EDT
From: [EMAIL PROTECTED]
Subject: Mersenne: Testing for factors
Now we can filter out multiples of small
Regarding the discussion about the distribution of M_p:
Sam Wagstaff's results imply that the expected number of
Mersenne primes between 2^h and 2^2h is exp(gamma).
Thus, they DO get progressively rarer.
Further, by the PNT, the probability that a random integer
near x is prime is
hi,
I'm sure that you all have calculators (hell, you all have some serious
PC's!), but e^{gamma} is approximately 1.781.
Maybe that was unnecessary,
Alan Simpson
___
Get Free Email and Do More On The Web. Visit http://www.msn.com
hi everyone,
there have been several messages lately about this conjecture that the n-th
Mersenne prime is "around" (3/2)^{n}.
However, no one seems to have mentioned Wagstaff's paper in Math. Comp.
(1982 or 1983).
He shows two things in this paper.
(1)he shows that an earlier conjecture
Alan Simpson wrote:
hi everyone,
there have been several messages lately about this conjecture that the n-th
Mersenne prime is "around" (3/2)^{n}.
(1)
However, no one seems to have mentioned Wagstaff's paper in Math. Comp.
(1982 or 1983).
...
(2)
. But do people have any
Uhh, yeah, I've got a 2^32 one, too and I can *make* any arbitrary part of a
2^64 one fairly quickly. :)
--
From: Jud McCranie[SMTP:[EMAIL PROTECTED]]
Sent: Wednesday, June 23, 1999 9:19 AM
To: Brian J. Beesley
Cc: [EMAIL PROTECTED]; [EMAIL PROTECTED]
Subject:
"Steinar H. Gunderson" [EMAIL PROTECTED] wrote:
My other (a PII/448) is currently...
448? That looks like the kind of MHz number that results from some kind of an
overclock...
Get free e-mail and a permanent address at
On Wed, 23 Jun 1999 01:42:08 PDT, you wrote:
hi everyone,
there have been several messages lately about this conjecture that the n-th
Mersenne prime is "around" (3/2)^{n}.
However, no one seems to have mentioned Wagstaff's paper in Math. Comp.
(1982 or 1983).
He shows two things in this
Hello,
This is slightly off topic so please bare with me. A side effect of having
Gimps on your computer is improved security. I have mine configured to be
a tray icon, which generally goes unnoticed or is ignored. If someone were
to steal my laptop (assuming they didn't reformat my hard
Well, my question is very simple. How can we see that 2*k*p+1 is composite?
Or is it composite for any special k like k=4*n ?
There is another constraint - 2kp+1 must be congruent to 1 or 7
modulo 8.
If p is congruent to 1 modulo 8, then for k = 0 (mod 4), 2kp+1 = 1
(mod 8); k = 1 (mod 4)
On Fri, Jun 18, 1999 at 01:00:20PM +1200, Halliday, Ian wrote:
ourworld.compuserve.com, the full URL of which nobody ever seemed to
remember. Now I'm in the same boat as S Gunderson, who has switched to
double checking because he doesn't like having to wait months for a result.
You're certainly
On Tue, Jun 22, 1999 at 12:23:47AM +0100, Gordon Spence wrote:
I think the point is to hammer into Aarons skull that what he did was wrong
period.
By doing the same yourself? No, let us please let this discussion drop.
Anyway if it turns up some new factors, then that is advancing scientific
On Tue, Jun 22, 1999 at 06:56:42AM +0100, Brian J. Beesley wrote:
There is another constraint - 2kp+1 must be congruent to 1 or 7
modulo 8.
Here comes something that has been confused me for a long time. Isn't
1 modulo 8 = 1? You are always talking about `1 modulo something'.
My definition of
At 01:21 PM 6/22/99 +0200, Steinar H. Gunderson wrote:
Here comes something that has been confused me for a long time. Isn't
1 modulo 8 = 1? You are always talking about `1 modulo something'.
Almost always it is something modulo something else is congruent to 1.
From: Steinar H. Gunderson [mailto:[EMAIL PROTECTED]]
On Tue, Jun 22, 1999 at 06:56:42AM +0100, Brian J. Beesley wrote:
There is another constraint - 2kp+1 must be congruent to 1 or 7
modulo 8.
Here comes something that has been confused me for a long time. Isn't
1 modulo 8 = 1? You are
For those of you who read PC Magazine, there is a short column by Bill
Machrone in the July 1999 issue on page 85 that talks about GIMPS, Aaron
Blosser, and the US West episode. Not a detailed examination of what
happened but some good press on why you might want to participate in such a
Yes, S.T.L: is right, and I believe that more can be done.
No two Mersenne primes can have the same prime divisor, as I recall. So by
listing the composite Mersenne primes (i.e., p is prime but 2^p -1 is not
prime), we can get a list of primes that no longer need to be tried as
divisors of 2^p
No two Mersenne primes can have the same prime divisor, as I recall. So by
listing the composite Mersenne primes (i.e., p is prime but 2^p -1 is not
prime), we can get a list of primes that no longer need to be tried as
divisors of 2^p - 1. So sure, use the +/-1 mod 8 rules, eliminating a
On 22 Jun 99, at 20:30, [EMAIL PROTECTED] wrote:
Now we can filter out multiples of small primes
I'm assuming that we don't need to divide by factors divisible by 3 or 5,
etc, because a Mersenne number cannot be divisible by 3 or 5 because they
don't have the structure 2kp+1 themselves?
On 22 Jun 99, at 17:38, Gary Diehl wrote:
1. Why only put the first six prime numbers in the sieve table? (Don't
you want to eliminate other prime numbers too, or am I missing a bigger
issue here?)
For a 1-pass sieve table, the table size is the product of the
numbers you're sieving out.
Hi,
At 12:42 AM 6/21/99 +0200, Otto Bruggeman wrote:
Sorry to bother you people with this but can anybody tell me why my celeron
400 all of a sudden slows to (almost) half speed when it reaches the
1,000,000,000 (actually a little more, i guess it's around 2^30) mark in
factoring numbers??? My
Hi,
Thanks for answering my question... But this brings me to another one :
Wouldn't it be better to first do factoring till 2^62 and then do the the
ones above 2 ^62 ??? Just for Celerons and other high clock multiplyer
processors, or is that impossible with the the program ??? I think this
Now, since my version for some reason is faster than George's (2-3% on LL
tests, 6-7% on factoring; I have no clue why), I don't really like going
back to a slower version.
I have played around with the Prime95 V18.1 found a simular improvement
in compiling on a more recent compiler (MS VC++
Date: Mon, 14 Jun 1999 15:21:52 -0700
From: Will Edgington [EMAIL PROTECTED]
Subject: Mersenne: Re: factoring 10^7 digits (was LL and factoring
quitting)
We will of course have to check factors considerably further than
we are doing on our current exponent range (due to the increased
At 10:54 PM 6/21/99 +0100, Gordon Spence wrote:
Yup. And don't forget that the larger the exponent, the fewer the
possible factors in a given range (e.g., from 0 to 2^40 or 0 to 2^63).
Ok, I'll ask the stupid question, I stopped maths at the year before
university, WHY is this the case?
Listen, everyone, please stop. It has been requested on this group that
this topic be dropped. Please, please, have the decency to let this topic
go. If you *must* discuss it, keep it off the list in private emails.
Please remember that a message written in anger is *never* on topic--well,
in
On Mon, Jun 21, 1999 at 11:03:13PM +0100, Gordon Spence wrote:
I have access for a while to about 3 dozen quad P3-450 boxes. I had thought
about taking *ALL* the numbers that Aaron is running for his testing and
running them on these machines. So that when he checks them in, he finds
that they
From: Jud McCranie[SMTP:[EMAIL PROTECTED]]
At 10:54 PM 6/21/99 +0100, Gordon Spence wrote:
Yup. And don't forget that the larger the exponent, the fewer the
possible factors in a given range (e.g., from 0 to 2^40 or 0 to 2^63).
Ok, I'll ask the stupid question, I stopped maths
Yup. And don't forget that the larger the exponent, the fewer the
possible factors in a given range (e.g., from 0 to 2^40 or 0 to 2^63).
Ok, I'll ask the stupid question, I stopped maths at the year before
university, WHY is this the case?
Because a factor of Mp must be of the form 2*k*p+1
At 06:33 PM 1999/06/21 -0500, "Willmore, David" [EMAIL PROTECTED] wrote:
Ahhh, because the smallest factor must be = the sqrt() of the number!
Sorry, Gordon, I was wondering the same thing when you asked this. :)
Um, no. For exponents of current interest, p~=7,000,000,
Mp=2^p-1 has p bits, and
At 06:33 PM 6/21/99 -0500, Willmore, David wrote:
Ahhh, because the smallest factor must be = the sqrt() of the number!
Yes, but that doesn't matter here. We are checking for divisors less than some
relatively small limit (much smaller than the number itself). For a given
limit, there are
At 07:39 PM 6/21/99 -0400, lrwiman wrote:
Actually, it 2*k*p+1 must be ==+/-1 mod 8 which is 2/8=1/4. This can be
further reduced by checking for divisibility by 3, and 5.
So thats 1/(15*p) of numbers that we are actually checking.
Yes, but the crucial thing in answering his question is the
Hi Otto,
At 08:07 PM 6/21/99 +0200, Otto Bruggeman wrote:
Wouldn't it be better to first do factoring till 2^62 and then do the the
ones above 2 ^62 ???
This oft asked for feature is already implemented in v19. If an exponent
is already factored to 2^55, then it does all 16 passes to 2^56,
I have found 12,209 new factors in the range of Brian's 10,000,000+ digit.
All of the other primes in this ranges have tested through 2^45.
They are avalaible at:
http://www.tasam.com/~lrwiman/fact45
or
http://www.tasam.com/~lrwiman/fact45.gz
These just include the new factors.
-Lucas Wiman
It's "testing" 2^25,000,009 - 1 right now. It can test one factor every 1.3
seconds. AUGH! At that rate it would take 95 *billion* years to trial divide
by all odd numbers under 2^62. Nooo
Don't forget, it's not just odd numbers, you only need to trial divide by
numbers that end in 1, 3,
Great! Can we get FPGA chips at Digikey or Mouser? How much do they go
for?
-Chuck
On Fri, 18 Jun 1999, Aaron Blosser wrote:
My understanding is that it comes with a language of its own. My
impression is that it is an icon based language. Kind of like connect the
blocks into a flow
The one I used is from Viewlogic (www.viewlogic.com). They have a full set
of programs for designing, simulating, routing and programming FPGA's. It
is a VERY nice set of tools, but as you might guess, VERY expensive as well.
I did just order a 30 day evaluation CD from them though...it's
Will change the "engine" to keep going to 2^33 after finding the
first factor report the results from that.
OK, here's the results. (All factors to 2^33 found, input is 159,975
largest primes 36 million)
Sieve 6 smallest primes, 3517525 calls, 40.15s
Sieve 10 smallest primes, 2972446
Brian J. Beesley writes:
I put a development version on my anon ftp server about three days
ago. ftp://lettuce.edsc.ulst.ac.uk/gimps/DecaMega/factor95.c
Um, that's an unfortunate choice of name; George's P-1 factorer is
"Factor95" (though there's a newer version, renamed to Factor98).
Only HP and Solaris. :( Why don't they release the source and let me
compile it
myself? Maybe gEDA will include such a program.
if you are paying $50,000 to $100,000 a seat for a program, you BUY the
computer it needs.
Other vendors of similar FPGA software include Vantis (formerly AMD's PAL
At 12:42 AM 6/21/99 +0200, Otto Bruggeman wrote:
Sorry to bother you people with this but can anybody tell me why my celeron
400 all of a sudden slows to (almost) half speed when it reaches the
1,000,000,000 (actually a little more, i guess it's around 2^30) mark in
factoring numbers??? My
At 03:53 PM 6/20/99 -0700, Luke Welsh wrote:
As long as we're fitting data to a curve, how about substituting
pi/2 for 3/2?
If you fit the curve to the data, 3/2 works a lot better. The best fit is for
a slope of 1.4785, which has a very high correlation coefficient of 0.996.
Mersenne Digest Sunday, June 20 1999 Volume 01 : Number 585
--
Date: Sat, 19 Jun 1999 13:43:34 -0700
From: Will Edgington [EMAIL PROTECTED]
Subject: Re: Mersenne: TI-92 Factoring, again
Brian J. Beesley
Sorry to bother you people with this but can anybody tell me why my celeron
400 all of a sudden slows to (almost) half speed when it reaches the
1,000,000,000 (actually a little more, i guess it's around 2^30) mark in
factoring numbers??? My p233mmx slows about 15 percent.
I'm just
At 08:41 PM 6/20/99 -0400, lrwiman wrote:
Doubtful, since the LL remainder never goes above Mp. The only thing that
inherantly increases is the iteration count, which takes up about log_2(p)
bits. Not that much...
P.S. 2^30 is ~100,000,000
not ~1,000,000
Actually 2^30 is ~ 1,000,000,000.
Sorry to bother you people with this but can anybody tell me why my celeron
400 all of a sudden slows to (almost) half speed when it reaches the
1,000,000,000 (actually a little more, i guess it's around 2^30) mark in
factoring numbers??? My p233mmx slows about 15 percent. The numbers
currently
If it really is that bad, then it's probably not worth doing. I once
tested all the prime exponent Mersennes with exponents from about 10
million thru about 21 million for factors smaller than 2^33 or so,
using mersfacgmp on a Pentium 90MHz, in a couple of days.
The factoring program I used
Will Edgington commented:
Chris Nash writes:
The smallest factor of 2^p-1, p a prime, is at least as big as
2p+1. All factors of a Mersenne number of prime exponent are of the
form 2kp+1 - similarly for all 'new' factors of a composite
exponent (ie that haven't appeared in any
[EMAIL PROTECTED] writes:
Using the wonderful modpwr() from Paul Pollack's NTH library for
the TI-92, I have quickly verified the following results I found on
Entropia.com: [...]
Good.:)
For each of them, the TI-92 quickly returned that 2^exponent mod
factor = 1, and very
However, a semi-reasonable task would be to test numbers for factors up to
2^16.
Done.
Pitiful, I know, but a TI could test a single number in 12 hours.
An optimized algorithm will do it in about zero seconds.
B) To Mr. Woltman or Mr. Kurowski - how "useful" would factoring (most
likely
Foghorn Leghorn writes:
Could you factor a Mersenne number without storing it in memory?
(Answer: I don't *think* so) Ptoo bad. If we could factor
Mersenne numbers on an unmodified TI-92+, then there'd be a lot of
people who'd run that program.
Uh, that's exactly what
[EMAIL PROTECTED] writes:
So, is this:
(2^p mod f) - 1
Congruent to this:
(2^p -1) mod f
Yes, though be careful about the case of 2^p mod f being 0. The first
will give you -1 and the second is f-1. They are congruent, mod f, of
course, but not identical.
This is doubly
Using the wonderful modpwr() from Paul Pollack's NTH library for the TI-92, I
have quickly verified the following results I found on Entropia.com:
7017133 61 F 1901619961404080441 14-May-99 11:35 jay2001
PII_40
7029787 62 F 3764452186385609519 31-May-99
Also, to ease finding factors, using a number which is a multiple of 8 is
a good idea. However, how much work has been done on checking other mods
other than 120? Like 80, or even 720 to see what happens? just
wondering...
As often happens (to me at least), as soon as I tell someone
If you take the following comma delimited file into a spreadsheet, and
graph it (say with a line chart) it shows the relationship of Mersenne
exponents to their index, for the first 37 Mersenne primes. The first
column is the log of (3/2)^n, the second column is the log of the exponent
of
Brian J. Beesley writes:
If it really is that bad, then it's probably not worth doing. I once
tested all the prime exponent Mersennes with exponents from about 10
million thru about 21 million for factors smaller than 2^33 or so,
using mersfacgmp on a Pentium 90MHz, in a couple
For those of you who read PC Magazine, there is a short column by Bill
Machrone in the July 1999 issue on page 85 that talks about GIMPS, Aaron
Blosser, and the US West episode. Not a detailed examination of what
happened but some good press on why you might want to participate
in such a
Well, looks like factoring on TI calculators won't be feasible or useful. :-(
Before more data comes in, I'd like to state that I believe three things:
A) The 38th Mersenne prime discovered has an exponent in the neighborhood of
6,900,000.
B) We *are* missing a Mersenne prime between 3021377
On Thu, Jun 17, 1999 at 01:11:09PM -0400, Jud McCranie wrote:
The IA-64 sounds like a monster. I'll want one, but they'll probably be too
expensive for a few years. (It happens over and over - "no person will need
that much on their desktop.")
In the case of the 386, there was "no person will
On Thu, Jun 17, 1999 at 09:21:57AM -0700, John R Pierce wrote:
where Z is a 256 bit 'accumulator'...
And where are you going to find a 256 bit add instruction? :-)
/* Steinar */
Unsubscribe list info --
On Fri, 18 Jun 1999, Rick Pali wrote:
From: Robert Stalzer
Once I've 'Cleared' an unwanted exponent from my to-do list
('oops, didn't want to do double-checks') how do I banish the
outcast exponent from my team's report?
The easiest way is to make sure that your instance of the prime
I'm Sylvain Perez, I do take care of the French version of GIMPS.
If any of you need francophone support, please visit
http://www.entropia.com/gimps/fr, or send me an email.
About cool guys that like hot chips, what do you think about those pages :
http://www.agaweb.com/coolcpu/, it seems to
According to the FAQ, "PrimeNet knows when a test result was computed on a
different computer. It will accept your results for the master database
log, but it will not credit your account for the test work."
(1) Does this cause a credit problem when a team member gives 2 PCs the
same Computer
Mersenne Digest Friday, June 18 1999 Volume 01 : Number 583
--
Date: Thu, 17 Jun 1999 23:38:11 +0100
From: Nick Craig-Wood [EMAIL PROTECTED]
Subject: Re: Mersenne: Thoughts on Merced / IA-64
On Thu, Jun 17,
- 82bit FPU (??)
82 bits? It is time to go to 128 bits!
*If* the IA64 has a fast pipelineable 64 bit * 64 bit - 128 bit integer
multiply capability, perhaps the FPU is no longer needed? I guess I'd
better dig into that Architecture document a bit more. Ah, sigh. It has
64*64 but it only
At 11:36 PM 6/16/99 -0700, John R Pierce wrote:
*If* the IA64 has a fast pipelineable 64 bit * 64 bit - 128 bit integer
multiply capability, perhaps the FPU is no longer needed?
You still need floating point numbers and that's probably better handled with
FPU hardware.
-Original Message-
From: Aaron Blosser [mailto:[EMAIL PROTECTED]]
Sent: Wednesday, June 16, 1999 10:32 PM
To: Mersenne@Base. Com
Subject: RE: Mersenne: Z80s Are Everywhere!
guess you might even be able to find the odd one [Z80
processor] still in use somewhere
Actually,
From: Jud McCranie[SMTP:[EMAIL PROTECTED]]
At 11:36 PM 6/16/99 -0700, John R Pierce wrote:
*If* the IA64 has a fast pipelineable 64 bit * 64 bit - 128 bit integer
multiply capability, perhaps the FPU is no longer needed?
You still need floating point numbers and that's probably
On Thu, 17 Jun 1999, Halliday, Ian wrote:
Some considerable while back, there was a lively discussion as to the
_total_ number of Mersenne primes. I still believe that the number is
finite, in contrast to what appears to be the majority view: that there is
an infinity of Mersenne primes out
At 11:36 PM 6/16/99 -0700, John R Pierce wrote:
*If* the IA64 has a fast pipelineable 64 bit * 64 bit - 128 bit integer
multiply capability, perhaps the FPU is no longer needed?
You still need floating point numbers and that's probably better handled
with
FPU hardware.
Do you? I thought
At 11:02 AM 6/17/99 -0500, Willmore, David wrote:
No, no, no, no. :)
I'm speaking that in general you need FP hardware.
Georges code uses the FPU of intel chips because the
early ones had very poor integer processing capabilities
The Intel FPU is still better at handling 64-bit integers than
At 09:21 AM 6/17/99 -0700, John R Pierce wrote:
You still need floating point numbers and that's probably better handled
with
FPU hardware.
Do you?
Yes. You absolutely need FP numbers, and in all cases that I know of, FP
numbers are better handled by FP hardware.
-Original Message-
From: Jud McCranie [mailto:[EMAIL PROTECTED]]
Sent: Thursday, June 17, 1999 12:25 PM
To: John R Pierce
Cc: Mersenne discussion list
Subject: Re: Mersenne: Thoughts on Merced / IA-64
At 09:21 AM 6/17/99 -0700, John R Pierce wrote:
You still need floating
On 17 Jun 99, at 13:36, Halliday, Ian wrote:
Some considerable while back, there was a lively discussion as to the
_total_ number of Mersenne primes. I still believe that the number is
finite, in contrast to what appears to be the majority view: that there is
an infinity of Mersenne primes
Do you? I thought the only reason the FFT was using FP numbers was most
current generation processors have a faster and higher precision FP multiply
than fixed point. With a 64*64 bit fixed point multiply that generates a
higher precision result, you can quickly do exact fixed point
Aaron Blosser wrote:
BTW - Read http://www.cnn.com/TECH/computing/9906/15/supercomp.idg/
I am reminded of hype over the "thinking machines" parallel computer.
How difficult is it to write for an FPGA array? Do tools exist to
compile a C program into an FPGA configuration? Has BEos been
-Original Message-
From: Pierre Abbat [mailto:[EMAIL PROTECTED]]
Sent: Thursday, June 17, 1999 2:24 PM
To: Blosser, Jeremy; Mersenne discussion list
Subject: RE: Mersenne: Thoughts on Merced / IA-64
You could go with a NTT instead of a FFT. Thus foregoing any double
precision
At 09:21 AM 6/17/99 -0700, jrp wrote:
[...]multiplying 2 128 bit integers X * Y where Xh and Xl are the high
and low half of the X argument takes 4 multiples plus a few adds.
It can be done in fewer than 4 muliplies. See Karatsuba's Method in
Knuth's TAOCP, Vol 2, Section 4.3.3, "How Fast Can
On Thu, 17 Jun 1999, Blosser, Jeremy wrote:
See: http://www.hut.fi/~mtommila/ntt.html for a decent explanation of an NTT
and how it relates to FFTs. At some point GIMPS would either have to move to
quad precision primes or an NTT algorithm because of round-off errors (not
enough bits... I
On 17 Jun 99, at 19:48, David L. Nicol wrote:
How difficult is it to write for an FPGA array? Do tools exist to
compile a C program into an FPGA configuration? Has BEos been ported
to it?
Basically what you have to do is to feed instructions which the FPGA
can execute from firmware
On Thu, Jun 17, 1999 at 02:08:29PM -0700, Luke Welsh wrote:
BTW, has anybody investigated this package:
http://clisp.cons.org/~haible/packages-cln-README.html
Yes I have.
It is a very thorough C++ class library for number manipulation. It
has an O(n log n) multiply. You could
On Thu, Jun 17, 1999 at 11:09:12PM +0100, Brian J. Beesley wrote:
When you do your NTT, you're going to need at least twice as many
bits in the elements of the transform as there are bits in the number
you're testing (because you're going to want to square the values in
the elements,
But, you can do it in integer if you have a processor with 1)
enough integer
registers 2) wide registers and 3) fast/pipelined multiply--which IA-64 is
supposed to have. The floating point version was a cluge to make
up for an,
uhhh, *interesting* processor archetecture. It shouldn't make
Mersenne DigestThursday, June 17 1999Volume 01 : Number 582
--
Date: Wed, 16 Jun 1999 21:19:43 -0400
From: Brian Beuning [EMAIL PROTECTED]
Subject: Re: Mersenne: $1000 supercomputer
They seem to be
Here at the University of Michigan, there are computer labs with Dell
Pentium II systems running Windows NT 4.0. Each student has a little
online file space connected to the Sun login machines; I believe it uses
the Andrew File System (AFS). This file space is made available as a
network drive
I still believe that the number is finite, in contrast to what appears to
be the majority view
The "majority view" is the way it is because a number of Darn Good (TM)
heuristic arguments have been made that the number of Mersenne Primes is
infinite, just like Darn Good (TM) heuristic arguments
Merely expressing an opinion as to whether or not you think there are an
infinite or finite number of Mersenne primes doesn't add anything to the
discussion unless you can furnish some argument one way or the other. As
with many issues in pure mathematics, it is unlikely (but not impossible)
that
Could you
factor a Mersenne number without storing it in memory? (Answer: I don't
*think* so) Ptoo bad. If we could factor Mersenne numbers on an
unmodified TI-92+, then there'd be a lot of people who'd run that program.
Uh, that's exactly what Prime95 does. To test whether a potential
At 08:46 PM 6/17/99 -0400, [EMAIL PROTECTED] wrote:
The "majority view" is the way it is because a number of Darn Good (TM)
heuristic arguments have been made that the number of Mersenne Primes is
infinite,
Furthermore, I haven't seen any (good) argument at all as to why they should be
only
Once I've 'Cleared' an unwanted exponent from my to-do list ('oops, didn't
want to do double-checks') how do I banish the outcast exponent from my
team's report? Can another volunteer be assigned the exponent
automatically or must we wait for the exponent to expire (a lengthy wait)?
Robert
From: Robert Stalzer
Once I've 'Cleared' an unwanted exponent from my to-do list
('oops, didn't want to do double-checks') how do I banish the
outcast exponent from my team's report?
The easiest way is to make sure that your instance of the prime software
has as many days of work as you've
Once I've 'Cleared' an unwanted exponent from my to-do list ('oops, didn't
want to do double-checks') how do I banish the outcast exponent from my
team's report? Can another volunteer be assigned the exponent
automatically or must we wait for the exponent to expire (a lengthy wait)?
Go to
B: Cycling before the P-1th iteration is unlikely in its own right.
I thought we had more or less worked out (not formally proved - but a
solid argument)
At the time, Chris Nash said:
Who, me? I did a lot of hand-waving... Peter-Lawrence Montgomery followed up
with a couple of
"David A. Miller" wrote:
In response to a recent suggestion by Paul Leyland, I've been focusing my
ECM work on P773. I checked George's ECM status page tonight, and it lists
an astonishing 7210 completed curves at B1=11E6. Is this an error, or has
someone been putting a ton of machines to
At 09:56 PM 6/15/99 -0700, Rudy Ruiz wrote:
Notwithstanding this, I believe that those 35 souls that are still
owing exponents, should be looked upon. Perhaps some have completely
stalled. The computer might not be connected to the internet anymore or
some funny mishap might be preventing them
P.S. - Nice to see that GIMPSers aren't cold calculating
mathematicians only!
Mathematicians don't have to be cold or uninteresting. Our maths teacher
cycles a 540km race every year, puts Zalo (that's the stuff you do your
dishwashing with in Norway) in her hair to increase the speed and is
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