On Saturday 01 February 2003 07:53, Eric Hahn wrote:
Let's say you've done 700 curves with B1=25,000 to
find a factor up to 30-digits... and you've been
unsuccessful... :-(
Now you've decided to try 1800 curves with
B1=1,000,000 to try and find a factor up to
35-digits.
Do you have to
Not knowing a whole lot about ECM... I thought I'd
ask this question... and maybe put out a new topic
to discuss... ;-)
Let's say you've done 700 curves with B1=25,000 to
find a factor up to 30-digits... and you've been
unsuccessful... :-(
Now you've decided to try 1800 curves with
B1=1,000,000
Hello, everyone!
I sent a letter to this list about a month ago indicating that Fermat number
factoring by the Elliptic Curve Method could be done more efficiently by running
curves on numbers of the form 2^(2^n) - 1 (M-numbers) instead of running on the
Fermat numbers themselves of the
I think I know the answer to this... but want to
double-check to be sure...
While doing factoring... using ECM... factors up to:
15 digits is the equivalent of ~2^50...
20 digits is the equivalent of ~2^67...
25 digits is the equivalent of ~2^83...
30 digits is the equivalent of
If trial-factoring has been done up to 2^68... is it
possible to skip testing ECM curves for factors up to 15
and/or 20 digits... and go straight to testing ECM curves
for digits up to 25 digits???
Personally, I would go straight in at the 25+ digits level.
OTOH, if trial factoring has
If trial-factoring has been done up to 2^68... is it
possible to skip testing ECM curves for factors up to 15
and/or 20 digits... and go straight to testing ECM curves
for digits up to 25 digits???
Personally, I would go straight in at the 25+ digits level.
OTOH, if trial
OK...
I think I know the answer to this... but want to
double-check to be sure...
While doing factoring... using ECM... factors up to:
15 digits is the equivalent of ~2^50...
20 digits is the equivalent of ~2^67...
25 digits is the equivalent of ~2^83...
30 digits is the equivalent of
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
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.
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.
I've been making an effort
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
I've been carrying out ECM for some time now on small exponents (under
40,000) and I'm curious about the amount of memory that it uses.
According to readme.txt, the minimum memory required is 192 times the FFT
size. For the exponents I'm looking at, I suspect that the FFT size is of
order a
Hi,
At 10:08 AM 3/29/2001 +1000, Steve Phipps wrote:
For the exponents I'm looking at, I suspect that the FFT size is of
order a kilobyte (BTW, can I look the FFT sizes and breakpoints up
somewhere?) and so the minimum memory required is less than 1MB.
A size 1024 FFT can handle exponents up to
The last machine that I had working on M727 has finished its 1000 curves
at B1=44M. This is enough to finish the recommended number of curves at
that bound. Thus there are probably no factors below 10^50, and it won't
be practical to find the factors with ECM.
Have any other numbers received as
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
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
And quite right too. It's just plain wrong. ECM runs in sub-exponential
How long will each ECM curve on M727 take? I'd like to run a few in May,
when I'm done with my current work, but don't know how many to set up. To
put it another way, how many curves will take about a week on a p3-600
running 16/7?
I checked the various FAQs, but couldn't find this
Hi, I need some help.
I would like to look for a factor of a mersenne prime in a specific area.
For example, for a mersenne exponent of say 40,000,000. I want to use the
Prime95b program, (v19 I guess), to search for a factor in a specific range
from, say, 2^40 to 2^50. I do not understand the
I would like to look for a factor of a mersenne prime in a specific area.
For example, for a mersenne exponent of say 40,000,000. I want to use the
Prime95b program, (v19 I guess), to search for a factor in a specific range
from, say, 2^40 to 2^50. I do not understand the ECM factoring
When this is cleared up, it will make a good FAQ.
Who maintains the FAQ list? Do you agree the answer here is a good FAQ?
At 01:10 PM 10/2/99 -0700, you wrote:
Hi, I need some help.
I would like to look for a factor of a mersenne prime in a specific area.
For example, for a mersenne exponent
When this is cleared up, it will make a good FAQ.
Who maintains the FAQ list? Do you agree the answer here is a good FAQ?
I would like to look for a factor of a mersenne prime in a specific area.
For example, for a mersenne exponent of say 40,000,000. I want to use the
Prime95b
"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
Hi all,
I have a different question concerning P-1 and ECM.
Some time ago I asked which power to put small primes
into when multiplying them into E ( factor = gcd(a^E-1,N) ).
Paul Leyland, I believe, replied that the power for prime p should
be trunc( ln(B1) / ln(p) ) ( log(B1) with base p ),
The function being minimized, namely
probability of finding a 50-digit factor on one curve
-
time per curve
is flat near its minimum. Implementation and platform differences
can obviously affect the denominator
At Paul Zimmerman's ECM page,
http://www.loria.fr/~zimmerma/records/ecmnet.html
the optimal B1 value listed for finding 50-digit factors is
4300, but
George's ECM factoring page uses 4400 for the same
purpose. Is one of
them wrong, or is there a reason for the difference?
At Paul Zimmerman's ECM page,
http://www.loria.fr/~zimmerma/records/ecmnet.html
the optimal B1 value listed for finding 50-digit factors is 4300, but
George's ECM factoring page uses 4400 for the same purpose. Is one of
them wrong, or is there a reason for the difference?
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
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