Alexander Kruppa wrote:
Brian J. Beesley wrote:
Hi,
(1) Could someone with the required background please tidy up my logic
and prove that the assertion above is true i.e. there is no prime
2^p-1 with p 3 such that there are solutions to x^2 mod 2^p-1 =
2^((p+1)/2) + 2
I believe the idea
Bjoern Hoffmann wrote:
Hi,
I wondered if someone already have checked if the last mersenne
numbers +2 are double primes?
like 3+5, 5+7, 9+11, 11+13 or
824 633 702 441
and
824 633 702 443
regards
Bjoern
Mp + 2 is divisible by 3 for odd p and thus cannot be prime.
Mp - 2 however can, in theory,
Daran wrote:
Peter Montgomery's dissertation, An FFT Extension to the Elliptic Curve
Method of Factorization,
ftp://ftp.cwi.nl/pub/pmontgom/ucladissertation.psl.gz ,
What do I need to read a psl file?
Ad far as I can see it is a regular PostScript. I don't know if the
extra l indicates
George Woltman wrote:
At 10:31 PM 12/3/2002 +, Daran wrote:
The analysis is more complex than this. It really depends on the prime
[...]
I'd be greatly interested in such a study.
Peter Montgomery's dissertation, An FFT Extension to the Elliptic Curve
Method of Factorization,
Gareth Randall wrote:
A short time ago there was a discussion relating to the prime95 process
running as System on NT/2000, and the subject of security issues
relating to it being accessible from a normal user's desktop came up.
The article linked below describes a serious security issue
Steinar H. Gunderson wrote:
On Thu, Aug 01, 2002 at 07:01:04AM -0700, Gary Edstrom wrote:
I seem to remember reading that there are probabilistic tests that can
be run on a number. The test is repeated for a number of iterations.
If the test fails any iteration, then it is definitely NOT
[EMAIL PROTECTED] wrote:
*** Intrinsity Arrays 2GHz Adaptive Matrix ***
(rest snipped)
Man, who comes up with these stupid soundalike Silicon Valley
Tech Company names? Is this some popular Java Applet CEOs
are using, which combines various techy-sounding word fragments to
generate
There was an article on Slashdot (http://slashdot.org) recently about a
paper by Daniel Bernstein which stirred people in the cryptograpy
business by claiming that with custom designed hardware, numbers three
times as large as are feasible today could be factored.
There is a new article on
Will Edgington wrote:
Is it worthwhile mounting a formal attack on the Mersenne numbers
between 20 million say 40 million using this technique? We're
getting quite close to this I think Chris would not have bothered
with these, since they were so far ahead of LL testing at
Bruce Leenstra wrote:
As luck would have it, this is nearly what I am doing right now:
tempvalue = (q+1)/2
count = 1
while tempvalue != 1 {
if tempvalue is odd tempvalue += q
shiftright tempvalue
count++
}
v = count
I'm not sure I understand that code yet, but
I've
That paper sounds like a genuine revolution.
I have looked at two papers of Bernstein before, Prime Sieves Using
Binary Quadratic Forms together with A.O.L. Atkin (algorithm a.k.a.
Sieve of Atkin, implementation by Bernstein available under the name
primegen), and How to Find Small Factors of
[EMAIL PROTECTED] wrote:
On 26 Feb 2002, at 19:46, Henk Stokhorst wrote:
http://slashdot.org
factoring breakthrough?
Doesn't look like a breakthrough, although there may be a very
significant reduction in the amount of work required to factor
awkward numbers.
The implications
Steve Harris wrote:
There is already a feature which does effectively the same thing. Set
'InterimFiles=100' in prime.ini and it will write a save file in the
working directory with a sequential extension every million iterations (or
however often you set it). You must manually edit
[EMAIL PROTECTED] wrote:
On 26 Jan 2002, at 14:45, John R Pierce wrote:
In any case it is rather doubtful that the compiler could make much
difference to Prime95. The pieces coded in C are of the run once
variety rather than being executed in every iteration.
That is true for LL testing
Torben Schlüntz 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 comprehensive archive of known Mersenne factors.
However, there's another generalisation that occurs to me that would be
quite cheap to implement. The purpose of stage two is to catch those
factors which are 'just out of reach' of stage 1. However another way a
factor could be 'just out of reach' would be if the power of exactly one of
Mary Conner wrote:
This exponent is not an isolated example. I have a printout of the first
page of the Assigned Exponents report from Dec 7th. I compared it with
the Assigned Exponents report from a few minutes ago, and three exponents
off that first page have moved from their old
Daran wrote:
- Original Message -
From: Alexander Kruppa [EMAIL PROTECTED]
To: Daran [EMAIL PROTECTED]; [EMAIL PROTECTED]
Sent: Monday, December 10, 2001 12:16 AM
Subject: Re: Mersenne: P-1 Stage 2
P-1 stage 1 computes x = a^E (mod N), where E is the product of all
primes
[EMAIL PROTECTED] wrote:
Dear All:
There were several toasts, including two synchrony
with a couple of groups of GIMPSers in Germany who
stayed up late to mark the occasion with us, lots of
good food and drink, and of course conversation about
primes (mostly shouted, as Tied House was
Daran wrote:
The math page http://www.mersenne.org/math.htm explains how to do a stage 1
P-1 test with given bound B1, but it omits the explanation of the
enhansement that uses B2 in stage 2. Anyone care to explain
how this is done?
Cheers
Daran G.
P-1 stage 1 computes x = a^E (mod
[EMAIL PROTECTED] wrote:
On 4 Dec 2001, at 17:59, George Woltman wrote:
Case 1: I finish first, find a prime and announce my discovery. I did
the work but the exponent is assigned to you! Who gets the
credit???
You, get the credit. User b will be mighty disheartened. I know first
Warut Roonguthai wrote:
http://www.academicpress.com/inscight/11302001/grapha.htm
Look like the cat is out of the bag now - it's 2^13,466,917 - 1. Was
this early publication indended? I thought the press release was due
only after the independent double check completed, but then they quote
Another other way to fix the problem is to have the compute-
intensive process voluntarily relinquish its timeslice at intervals
which are much shorter than the minimum timeslice (which is
typically of the order of 200 ms). This reduces the efficiency of the
compute-intensive task to some
Alexander Kruppa wrote:
gp_p(x) | go_p, and p+1-sqrt(p) = go_p = p+1+sqrt(p) . Since go_p(x)
Correction: I have taken the limits above from my memory which has once
again proved itself untrustworthy. The correct limits are
p+1-2*sqrt(p) go_p = p+1+2*sqrt(p) , a theorem by Haase, which I
Hi all,
I think I found a (although purely theoretical) way to find a factor of
M(p) by factoring M(M(p)).
Ok here goes:
f is a prime factor of M(M(p)),
2^(M(p)) = 1 (mod f)
so the order of 2 in Z/f*Z is !=1, divides M(p) but is not neccessarily
equal to M(p). Lets call it c.
Since the order
Steve Phipps wrote:
While we're on the subject, can someone explain how to derive the group
order for factors found using ECM? I've been carrying out ECM on an old PC
for almost a year now, and I'd like to be able to derive, and factorise,
the group orders for the factors that I've found.
Nathan Russell wrote:
Is it (at least) theoretically possible that some larger factors are
unfindable with ECM due to the limited number of sigma producable by
George's random number generator?
Nathan
I dont think this is a problem. Limits in the RNG would only mean
problems if it causes
Eric Hahn wrote:
If a person runs an ECM test using a B1 of 250,000 with 700
curves (for up to 30 digits), will they also find any factors
that they would have found if they had used a B1 of 50,000 with
300 curves (for up to 25 digits) ?!?
Eric
If the sigma is the same, then a curve
John R Pierce wrote:
The newest Geforce3 chip also has both Pixel Shaders and Vertex Shaders
which are each a SIMD programmable vector processors. The Pixel Shaders
operate on every pixel and generate the actual RGB pixels while the Vertex
Processors operate on the geometry and texture
Hello,
I have a question whether it is possible to uss the CRT to multiply
modulo a prime d.
\phi(d) = d-1, choose k so that there are primes p_1 .. p_n where (p_1
-1)*..*(p_n-1) = k*(d-1).
Now the system of congruences (mod p_i), i=1..n, will have a cardinality
that is a multiple of phi(d). Is
number whose
primality
status was unknown. That distinction now goes to F_33; a detailed list
of known factors and primality status of Fermat numbers can be found at
http://www.prothsearch.net/fermat.
The factor was found by Alexander Kruppa on one of five AMD Thunderbird
1GHz computers located
Compiling a forge version with malicious code of Prime95/mprime and
distributing it is maybe the simples and possibly most devastating
attack. Since the complete source (save for the Primenet checksums but
these could either be reverse-engineered or the fake client could simply
connect to a fake
"Brian J. Beesley" wrote:
(1) Removing these assignments from PrimeNet and managing them
seperately. Anyone who is prepared to make special arrangements to
acquire these assignments is unlikely to default by reason of lack of
commitment.
Someone is (or was?) doing something similar - David
"Brian J. Beesley" wrote:
On 4 Feb 2001, at 0:27, Alexander Kruppa wrote:
Well, you could bump NTprime's priority to 4; that would let NTprime
steal CPU cycles off the screensaver, without being too obvious to
the user :) Don't go any higher, as you would risk seriously
"Brian J. Beesley" wrote:
Some people have indicated they'd like a version of the program with
a pretty screen-saver interface. Fair enough, provided we can keep
the "classic" version without the extra overhead.
The screen-saver idea is important for another reason.
I asked several
I've read on the list some time ago that ECM takes, like Pollard-Rho or
P-1, O(sqrt(f)) operations mod N to find a factor f. But looking at the
factors found so far I find that hard to believe; according to that
formula, finding a 50-digit factor should be 10^15 times harder than
finding a
Matt Gauthier wrote:
In message [EMAIL PROTECTED], Mersenne Digest writes:
Do not "make clean" in linux/, this will remove all the FFT object files! Only
The latest version of gas can, apparantly, handle intel syntax with
the appropriate psuedo-op. I haven't looked into it, but it should be
Spike Jones wrote:
A few weeks ago, I thought someone posted something like:
2^n-1 where n is prime cannot have any factor smaller than n.
Did I get that right? Is there a simple proof? spike
Factors of a mersenne number Mp are always of the form f=2*p*k+1, k may be
as small as 1.
The
Andy wrote:
I'm trying to compile the source code for Prime95 for a wintel machine and
am slightly lost for how to do so. I have Visual C++, gcc, a86 and just
about everything else.
The Linux version should compile without too much hassle, but you have to
remove the calls to the SEC5
[EMAIL PROTECTED] wrote:
Thought: If a website uses images, does it necessarily have to care that
text-based browsers won't see them? No.
Yes. There are *many* blind people who rely on speech output of on-screen text.
A friend of mine gradually loses eyesight and is beginning to train for
Eric Hahn wrote:
Greetings all,
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?
Yup, each factor f, for which b^E == 1 (mod f) (b is the base, usually
3, E is
"Brian J. Beesley" wrote:
On 25 May 00, at 23:39, Ken Kriesel wrote:
I saw something similar once, out of hundreds of ECM curves
that I've run.
It happened on the curve being run while I adjusted memory limits
on the program (Version 20.4.1, April 25 file date), if I recall correctly.
Paul Leyland wrote:
It's well known that factors of M(p) are of the form 2kp+1.
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 who knows for certain reassure me that this has been done
George Woltman wrote:
Correct. However, if you do find a factor you will get credit. In fact
you get credit for trial factoring up to the size of the factor.
Umm.. I found some 30-digit factors with moderate bounds. Does that mean I'd get
credit for trial-factoring up to 100 bits? Trial
www.mersenne.org/ecmg.htm for current ECM factoring limits on Fermat numbers,
Oops, should read: ecmf.htm
Ciao,
Alex.
_
Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne Prime FAQ --
Nayan Hajratwala wrote:
problem; I need to find the largest known prime of the form:
(2^2^n)+1
congratulations by the way on finding the largest Mersenne prime!!!
These are Fermat numbers, Fermat conjectured that all numbers of this form
would be prime and proved it for
"Robert G. Wilson v" wrote:
Yes it is. In fact there are five numbers with this
characteristic. (10^n -1)/9 is prime when n is 2, 19, 23, 317 1031.
See "The Encyclopedia of Integer Sequences" sequence M2114, Neil J.A.
Sloane and Simon Plouffe, Academic Press, 1995.
Are all
Hi all,
I've been trying to figure out what the chance of finding a P-1 factor
is, given a certain amount of trial factoring and a P-1 bound.
I started with:
The chance of Mp having a factor in [2^n, 2^(n+1)] is 1/n.
The chance of a number N being B-smooth is
(log(B)/log(N))^(log(N)/log(B)) .
Gordon Spence wrote:
So how do we get to beg, borrow or steal time on this monster...
http://www.pcworld.com/pcwtoday/article/0,1510,14151,00.html
If they need code for a test drive, I could make a suggestion here..
hey, if David can do it..
Ciao,
Alex.
Hi,
the Lucas-Lehmer iteration
L_0 = 4
L_{n+1} = L_n ^2 -2
looks suspiciously like an iteration used in Pollard-Rho:
x_0 = a
x_{n+1} = x_n ^2 +b
Can this be used to do a LL test and Pollard-rho factoring attempt at
once?
I remember faintly having read something that b=-2 is not a good choice
Eric Hahn wrote:
I'm looking for program(s) capable of trial-factoring
prime exponent Mersenne numbers (using 2kp+1) meeting
the following requirements:
[factors and exponents of arbitrary size]
mersfacgmp from the Will Edgingtons mers package uses gmp's mpz type for
factors (thus the
Jason Stratos Papadopoulos wrote:
On Thu, 28 Oct 1999, Alexander Kruppa wrote:
Hi,
the Lucas-Lehmer iteration [...]
looks suspiciously like an iteration used in Pollard-Rho: [...]
Can this be used to do a LL test and Pollard-rho factoring attempt at
once?
Except that every
"Vincent J. Mooney Jr." wrote:
5 is an odd prime. 2^5 = 32 and minus one, is 31. 31 is not divisible by 3.
At 07:50 PM 10/26/99 +0200, you wrote:
Hello all,
a simple Number Theory question. Is always
(2^p-1) / p ,odd prime p, divisible by 3 ?
Well, I managed to mess up the
Hi,
I just tried a quick run of Georges new P-1 code on M(M(17)), and lo!
[cut]
At prime 499549. Time thusfar 1707.604 sec. (341520836670 clocks)
Stage 1 complete. 365804 transforms. Time: 1717.294 sec. (343458751180
clocks)
Stage 1 GCD complete. Time: 19.737 sec. (3947333454 clocks)
M131071
Morten Due Jorgensen wrote:
Given two programs, one running at normal priority, the other at the
lowest possible priority (idle priority), the second program will get
around 1-2% of the CPU,
I noticed the same thing under Linux (with rc5des). Idle processes get a
few % cpu time even on
Hi,
I´m thinking about something the would probably be called a stage 2 for
my P-1 factorer, i.e. the 3^(E*(p+x)) = 3^(E*p) * 3^(E+x) with x
difference between subsequent primes.
But I need to check for a factor after every of these steps, and a
full-blown GCD would be far too slow. Is there
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