Hoogendoorn, Sander writes:
Torben Schlaqntz wrote:
> It seems to me that this k (in 2kp+1) is never:
> 4,12,20,28,36,46,52,60,68,76,84
> at least for less than M416.947.
> Am I again a fool for a pattern already proved?
It has been proven that k = 1 or 7 mod 8
Careful! It
Alexander Kruppa writes:
Torben Schluntz wrote:
> I'd also like to know about any number fully factorized, whatever size
> it might be, and whatever size the factor(s) might be.
Try Will Edgingtons's page,
http://www.garlic.com/~wedgingt/mersenne.html .
Use used to keep a compr
Reto Keiser writes:
Where can I find the p-1 tool factor98.exe? As far as I know it
supports p-1 factoring furteher than prime95 (prime95 only allows a
b1 up to 700M). is this tool still available?
As Stefanovic as already replied, yes, it's still out there. Further,
I still have sever
Stefan Struiker writes:
When a requested factoring assignment is listed with, say, 52 in an
account log, does this mean it has been factored to 52 bits, but
_without_ success?
Yes, the number should have no factors less than 2^52.
Or could a factor have already been found in some ca
Trying to start a PrimeHunt on a Linux box, but can't find the
Gnome switch/requeste(o)r to get the screen resolution down enough
so I can read without a microscope. Can anyone help? Am running
Redhat 6.1 with a VooDoo 3500 GFX card.
Presuming you're running in an xterm window, try
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 sev
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. "Smo
Aaron Blosser writes:
I don't suppose George could just program something into the code
to have it check for the user being idle (like the screen saver
check does, but independent of the system screen saver routines)
such that if the user doesn't hit a key or move the mouse for xx
I've just updated my mersenne.html page, mostly by adding a new
section of "quick links" near the top that point to other people's
sites, including a new one for the factoring status of Fermat numbers
maintained by Jocelyn Larouche.
I also updated the data on M(M(p)) factoring progress and added
Brian J. Beesley writes:
On 15 Apr 00, at 4:22, Henrik Olsen wrote:
> I just tried downloading 20.3, both mprime and sprime, as well as tried
> with mprime 19.0.2 . None of them where able to detect the network as
> being available on a machine running Mandrake Linux, kernel version
Eric Bravick writes:
Is anyone actually working on the SPARC/Solaris client? I've seen
it under "coming soon" ever since I joined the effort. Speaking as
someone with a bunch of SPARC CPU's sitting around doing (almost)
nothing, I'm kind of interested in seeing this port...
Yes, a
P-1 on P727 with B1=30, B2=1
P727 stage 1 complete. 116 transforms. Time: 0.018 sec. (4659194 clocks)
Stage 1 GCD complete. Time: 0.001 sec. (164887 clocks)
P727 has a factor: 11633
This meets all the criteria too
1) 11633 is PRIME.
2) 2kp+1 = 2*(8)*727+1 = 11633
Paul Leyland writes:
A nasty thought just struck me.
It struck me in a different context some time ago; it might even be
archived.
When applying P-1 to mersenne numbers, an additional 2*p ought to
be included in the product, over and above all the powers of prime
< B1. Can anyone
Reto Keiser writes:
A lot of factors of exponents between 1 and 100 were found
using the new P-1 method. Is there a database which contains which
exponent were tested using which B1 and maybe a database od the
save files?
The P-1 data is also collected by me, in the 'o:' lin
Daniel Grace writes:
> Anyway, any mersenne's factor can be written as 2kp+1
> directly). Call (P-1)/p = Q
>
> Then 2n = Q mod p
> n = Q/2 mod p which is well defined
> Therefore we can find the sun of the two factors mod p.
I think what you are trying to say is
M_p
I've updated my web pages Yet Again, including adding some quick links
at the top of mersenne.html to the other Mersenne related files on my
web site.
The 1stfacnt.txt file is gone; I've split it into facntHU.txt (for
incompletely factored Mersennes) and facntD.txt (for completely
factored Merse
Eric Hahn writes:
I'm looking for program(s) capable of trial-factoring
prime exponent Mersenne numbers (using 2kp+1) meeting
the following requirements:
1) Capable of trial-factoring any exponent > 1
(at least to some considerably large number,
say 1 trillion?)
If y
Simon Burge writes:
Unless you're doing a timed run, maybe "kill -STOP pid" and "kill -START
pid" on the ecm3 run might give more accurate results - I hate to think
of what's happening to the cache... I use this on machines that have
mersenne1 running when users notice X load showin
Simon Burge writes:
Only runtime wisdom - Will didn't put tunefftw.c in the distribution.
If you or Will can send me a copy I'll try the tests again.
OK, I've ftp'd a new beta release that includes tunefftw.c and runs it
before doing the test of MacLucasFFTW.
I've kept a not-very-clos
I have ftp'd a new beta release of the mers package to:
http://www.garlic.com/~wedgingt/beta.tgz
beta.tar.gz
beta.zip
beta.shar
I'm announcing it to the mailing list because it includes a brand new
L
Will Edgington writes:
[Yes, I'm following up to my own message.:)]
n
p,pk1
,pk2
,pk3
Note that M(n) has no known factors.
Trying this out just now, the 111 MB of data that I have for prime
exponent Mersennes in the mersfmt reduces to a bit under 20 MB if this
format is
Brian J. Beesley writes:
1) I don't see any particular need to make available files in human-
readable format, provided that we provide a specification for the
file, and also binary executables for common platforms for converting
a machine-readable file to human-readbale format.
I
I have, just today (Sat., 25 Sept.), updated the mersdata file on my
web site; the lowM.txt file now contains all of the data that I have
for all Mersenne numbers with exponents thru 1 million, pushing the
size of the mersdata file (gzip'd or zip'd) to about 6.5 MB. That
pushes my usage to a bit
Pierre Abbat writes:
I suggest a couple of named pipes for control (the front end writes
to one and reads from the other, and mprime vice versa). Since
writing to a pipe whose reader is stuck can get you blocked when
the pipe is full, and writing to a pipe with nothing at the other
uot;residue" itself, including the beta
release's extract understanding the new P-1 save file format of George
Woltman's Prime95 v19. Extract's understanding of the P-1 save file
formats will be extended, when I get around to it, to converting from
one P-1 format to another.
Con
Keller (1983?)
M( M( 17 ) )H: 2^60 # Charles F. Kerchner III, Prime95, stopped
M( M( 17 ) )H: k=17592320263168 # "
M( M( 17 ) )o: 3961649 # (unknown, no P-1 save file)
M( M( 19 ) )C: 62914441 # k = 60, Raphael Robinson (1957)
M( M( 19 ) )C: 5746991873407# k = 5480769, Wi
Chris Nash writes:
I really hope that neither Will Edgington (with M(M(6972593))) nor Chip
Kerchner (with M(M(1398269))) dedicated any computer time whatsoever to
search for factors 2*k*M(p)+1 up to k=4.
I didn't, except perhaps to have mmtrial verify that the smaller k's
w
[EMAIL PROTECTED] writes:
> Am I correct? Or could a factor smaller than 2*k*p + 1 be missed in
> some cases?
In the last example a factor 16*97 + 1 could be missed.
Otherwise all factors below 2*k*p + 1 should be found.
One extra squaring will achieve the 2*k*p + 1 bound.
If I understand P-1 factoring correctly, then using it to a stage one
bound of k to try to factor M(p) will find all possible factors less
than or equal to 2*k*p + 1. I'm assuming that p is less than k (or p
is always used in the powering) and the convention several of us
agreed on a while back
The benchmarks site linked from www.mersenne.org:
http://www2.tripnet.se/~nlg/mersenne/benchmk.htm
... has not been updated in over a year. Is there an up to date one?
Further, the link there to another site for non Intel/Cyrix/Mac/AMD
systems at:
http://www.via.nl/users/mccidd/html/mersenne
Lucas Wiman writes:
Though I don't have specific timings, I imagine this would be the
case. I was referring to the Mfactor program by Peter Montgomery.
Oh. And I see he's already replied; from that info, I would guess
that Mfactor is only slightly faster than mersfacgmp on SPARCs (and
m
Lucas Wiman writes:
You could do factoring, the margin between factoring on a PC and an
UltraSPARC should be much slimmer than LL tests.
The last time I did timings like this - admittedly, probably over a
year ago, but the mers package hasn't changed much since, especially
in terms of per
Lucas Wiman writes:
I'm forced to agree with Aaron, aparently at gunpoint :-) (and I
said this a while ago, BTW). Even if they (George and Scott) did
this, then there would still be MacLucasUNIX, or everything else in
the mers package, as well as Ernst's program, and good ol' lucas.
Ken Kriesel writes:
I think Duncan Booth's name at least ought to be considered when
discussing the $ split. He wrote the first version of primenet
server and client; Scott Kurowski continued from the starting point
that Duncan provided. I suspect that Scott has considerably more
Kris Garrett writes:
Has it been proven that all mersenne numbers greater than one are
square free?
Depends on your definition of 'Mersenne numbers'. If you include
composite exponents, M(6) = 2^6 - 1 = 63 = 3*3*7 is not square free.
If you include only prime exponents, then you don't ne
[EMAIL PROTECTED] writes:
How about the No Icon option? (You can still access it by trying to
run Prime95.exe again). And have it configured as a Win95
service. I'm not sure if my system is an anomaly, but even the
Three-Fingered Salute doesn't show Prime95 to be on the list of
ta
Geoffrey Faivre-Malloy writes:
M16384 has a factor:
3178457030898592746194675570663374420833971377365687459461386297851584459031
8073180374859604847822828243686877928403667633015295
Further, if you try to divide this into M8192 (2^8192 - 1), you should
find that it factors that as well
Geoffrey Faivre-Malloy writes:
I found another factor for Fermat 16. What do I do now? How can I
factor this number that I found? Are there programs out there that
will let me do that?
Yes, there are such programs. One is ecmfactor, a program I maintain
as part of the mers package
Daren Scot Wilson writes:
I've switched from Linux to BeOS - entirely, not even dual-booting
both. Same hardware as before - PII 400 MHz. BeOS is POSIX
compatible, has TCP/IP, but the file system is offbeat, and from
what I hear most linux software needs a little bit of tweaking to
>>We will of course have to check factors considerably further than
>>we are doing on our current exponent range (due to the increased
>>LL iteration time.)
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
> Here are my ideas on bugs: Bugs happen! They're a fact of life,
> omnipresent in all software.
Showstopper bugs should not slip through testing and into release
software.
Correct: _should_ not. That does not mean _will_ not. Mistakes
happen, at least as often as accidents. If t
Luke Welsh writes:
TTBOMK, the theory was never formalized. Regardless, Peter Lawrence
Montgomery settled the issue:
http://www2.netdoor.com/~acurry/mersenne/archive2/0032.html
See also:
http://www2.netdoor.com/~acurry/mersenne/archive2/0035.html
http://www2.netdoo
Tony Forbes writes:
I know it's a bit feeble the usual standards for ECM factorization, but
Seems to me that "feeble" certainly doesn't include factors that are
new! Besides, I'm doing some work on 11-digit factors.:)
I just found this 36-digit factor of 2^2203+1 :
84842558947625500
Blosser, Jeremy writes:
So I ran JavaLucas with an FFT of 256k Its getting 1.75
sec/iteration. So... not too shabby really...
Not bad at all.
1) What the algorithm for finding the best FFT size. I was doing:
[...]
So I looked at MacLucasUNIX, and it has:
while (n < ((
[EMAIL PROTECTED] writes:
As LL tests begin to go beyond the limits of older machines, now may
be a good time to consider a distributed factoring effort. I've wanted
to see one for a while now but frankly, implementing many of the
algorithms is over my head. That, and the lack of a p
Alex Kruppa wrote:
Now I know how the 55 (mod 120) got there, it's:
M( 310169 )C: 3486114749130405725455
and the problem is that that's not a factor. Not remotely.
3486114749130405725455 = 2*3*11*69720503*757595229073 +1
so doesn't seem to be a factor of another Mersenne we've
Henk Stokhorst writes:
M(727) is not prime. VME made the claim that they could compute the
first prime following M(727) in two seconds. Just want to know
someone who can do the same trick and what software it takes.
It took less than 2 seconds to find the next sequential prime :
Sander Hoogendoorn writes:
Last weekend when i was testing Prime 95 i noticed that factoring
low numbers took much longer as high numbers.
Factoring M17XXX from 2^52 to 2^54 took minutes per pass while
factoring M9XX from 2^52 to 2^54 took about one minute to
complete the whol
Robert G. Wilson v, PhD ATP writes:
The below chart gives the general lower bounds for which the limit
of powers of two begins. As an example, 2^55 for the most part, is
the least exponent as a limit for all Mersenne numbers greater than
1,040,000. There are exceptions and this is
Simon Burge writes:
You may want to try what I do with some of our machines - instead
of killing and restarting the program, send it a STOP or a CONT
signal (I assume Linux has these signals available, I'm a BSD and
SysV person).
Yes, Linux has them, being a mostly POSIX-compliant U
Glenn Brown writes:
The computer has found TWO factors of 2^647+1. It's still
searching! WHY
Good question. Most likely, because what's left is still composite.
But since I don't know what program you're using nor what factors it
has found, I can't help you more without more inform
Don Leclair writes:
There is the risk that more than one factor (or all factors!) might
be extracted in between GCD's. This is easy to work around: After
each unsuccessful GCD, save the current iteration number. If the
next GCD(N,accumulator) is equal to 'N', back track to the
i
Tony Forbes writes:
I am looking for odd numbers n (not necessarily prime), n not divisible
by 3, n > 1000 such that both 2^n-1 and 2^n+1 have been completely
factorized into primes.
Look at the factoredM.txt file on my web pages. 2^n + 1 is listed
under 2^(2*n) - 1, from the differe
Nicolau C. Saldanha writes:
> > Given N, let f1(N) be the number of primes of the form 4n+1 which
> > are smaller than N, and f3(N) be the number of primes of the form
> > 4n+3 which are smaller than N. Thus, f1(10) = 1 and f3(10) = 2.
> > Is it true that f1(N) <= f3(N) fo
Paul Derbyshire writes:
[deleted]
Since you deleted all the text that you're replying to and your mailer
did not add to the 'References:' header, I cannot even be sure what
you are replying to, but I'll assume you're replying to me since I'm
the only one, as far as I noticed, that said anyth
Paul Derbyshire writes:
To list admins: Please fix the damn listserv software so it sets
Reply-To: to "[EMAIL PROTECTED]" will you? Right now it is
unintelligently just forwarding the messages, leaving the Reply-To
pointing at the author, and it is tedious to have to keep changing
Greg Hewgill writes:
Would MacLucas be suitable for double checking? Not having a Mac, I
have never run MacLucas, but there is lots of double checking work
going on right now in the 1.3e6 - 1.6e6 range.
I'm sure that there are quite a few people out there using
MacLucasUNIX for double
Alexander Kruppa writes:
I saw code posted earlier today that did LL testing with the GMP
library. It used the mpz_powm_ui function for exponentiating modulo
x. For x=2**p-1 this function can be sped up considerably, since a
mod (2^p-1) = a % 2^p + a / 2^p (integer operations) and t
Richard McDonald writes:
A bunch of Macs in my life would love to add to the effort, along
with my PCs. I've found the MacLucas program, which was never very
useable, is now unuseable; presumably the exponents are too large.
The MacLucasUNIX program of the mers package is a direct des
Paul Derbyshire writes:
I notice that GIMPS exponents are tested with a bit of trial
factoring and then we go straight to LL testing, without any
pseudoprime testing. I assume that pseudoprime tests are actually
slower than the LL test itself? Or else they'd use them to
eliminate
A week or so ago, I put a new release, v6.1, of the mers package on my
web pages at:
http://www.garlic.com/~wedgingt/mers.tgz
The prior (non-beta) release was v4.42; v5.x only appeared as beta
releases. There is already a newer beta release, as well.
Two new programs have been added since v4.4
Marc-Etienne Vargenau writes:
Yes, I have the same problem. With Netscape on Macinstosh or Unix
(Solaris). I sent a few days ago a private e-mail to George about
this and he answered that I was the only one to have this
problem. He told me that
ftp://gimps:[EMAIL PROTECTED]/home/
Henk Stokhorst writes:
table:1,7,17,23,31,41,47,49,71,73,79,89,97,103,113,119
In case it still isn't clear to someone out there, this is the list of
numbers less than 120 that are relatively prime (no common factors
greater than 1) to 120.
for number := first to last number in table do
Henk Stokhorst writes:
I simplified the code a little bit, it says divide, whereas in the
real code fourier transformations seem to be used. But I assumed
more people would be familiar with dividing than fourier
transformatios.
The factoring code does not use fourier transformations
I wrote:
Henk Stokhorst writes:
table:1,7,17,23,31,41,47,49,71,73,79,89,97,103,113,119
In case it still isn't clear to someone out there, this is the list
of numbers less than 120 that are relatively prime (no common
factors greater than 1) to 120.
Oops! I should have thoug
Bill Cherepy writes:
I recently join the project and I'm testing my first exponent. I
have two questions on Prime95.exe, the Windows 95 version.
Welcome!:)
When the program reached about 47% complete on the LL iterations,
Status listed a second exponent for me with a Dec date. It t
[EMAIL PROTECTED] writes:
I was looking at the available ranges to test Mersenne primes and
I noticed the range included exponents which by definition cannot
yield primes.
The ranges listed at www.mersenne.org and PrimeNet are mostly meant to
include only prime exponents. The
Foghorn Leghorn writes:
Second, I see that there are now some composite exponents in the
ECM factoring page. Why are none of them even? Is there a technical
reason that makes them less interesting?
As Sam Laur and George Woltman have mentioned, even exponent Mersennes
are always compos
Ken Kriesel writes:
M4190237 is not prime. Res64: 14FC0406840D6CF3. WQ1: 2DB378F5
(exponent) (result) (residue) (SW version) (security code)
Do other programs (MacLucas, mersenne1, etc.) have a security code,
or are those results on the honor system?
They are on the
gest that you do what I do for another no-email GIMPS member: use
the manual checkin & reservation page of PrimeNet. I created an
account for him with my email address and a name of 'His Name c/o Will
Edgington'; that way, I get the email warnings about exponents timing
out but I can
Brian J Beesley writes:
> It would also - improperly - catch those of us that can't use the
> automatic networking but whose machines are slower than the estimate
> for some reason. A participant without email access that sends me
> USMail with his data now and then is about to get
Brian J Beesley writes:
Also this would catch those users still using 15.x, which doesn't
have the same automatic mechanism for intermediate check-ins.
It would also - improperly - catch those of us that can't use the
automatic networking but whose machines are slower than the estimate
fo
I suppose the factoring methods do not guarantee to find _prime_
factors.
Correct. In fact, I recently added the ecmfactor program to the mers
package precisely because other programs, notably Factor98 (which uses
the P-1 method), print composite factors. I use ecmfactor routinely
(once
Yvan Dutil writes:
Maybe a multi-level objective would be better. Say for 2001:
-Exploration factoring up to 15 000 000
Depending on what you mean by "exploration", this is already done thru
21.5 million or so.
-one L-L up to 10 000 000
-two L-L up to 6 000 000
Others can almost
.
Note for Will Edgington: Will, I don't wanna die!! It's time to
upgrade MacLucasUnix! Or is it impossible??
I'm sure it's possible, but I certainly don't know enough to improve
the speed. And have not even had time to keep up with bug reports,
recently, though t
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