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
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?
