Many thanks to all the ECM curves with group orders that were sent to me
over the last week. I should have enough to build a reasonable QA suite.
_
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Merse
Brian
FYI I have directly computed the group order #E for each of your
factors/sigmas
below based on the Richard Crandall EC parameterization in Prime95.
They are:
M1123: #E = 777288435636813540 =
2^2*3*5*11*31*1823*38917*535489
M1621: #E = 649412561966194102824 =
2^3*3^2*11*857*3967*94727*
One more, this one is a much larger exponent.
The factor 17304916353938823097 of M111409 is found with
sigma=8866098559252914, in stage 2 with B1 >= 4861 & B2 >= 343351.
I didn't bother finding the critical limit for finding the factor in stage 1
as it would have taken a considerable amount of
Brian J. Beesley wrote:
After receiving this message, I removed _all_ the known factors for P721.
This was interesting, and indicates a bug, though it appears to be not very
important:
with same sigma & minimum B1 & B2 noted above, the composite factor 129
(= 3 * 43) was found. I would have e
On Sunday 10 November 2002 20:03, [EMAIL PROTECTED] wrote:
> "Brian J. Beesley" <[EMAIL PROTECTED]> wrote
> - Here's one example:
> -
> - With sigma=1459848859275459, Prime95 v22.12 finds the factor
> - 777288435261989969 of M1123:
> -
> - in stage 1 with B1 >= 535489
> - in stage 2 with B1 >= 3891
Hi George
I can supply working examples for ECM on 2^m+1 or more specifically for
Fm = 2^(2^m)+1 cases for known factors of Fermat Numbers from F10 to F23.
I can provide sets with (Fm, prime factor, sigma, smooth ECM group order).
I just need to verify them with Prime95 v22.12 to avoid any egg-on-
Brian
For M1123 the factor 777288435261989969 using sigma = 1459848859275459 has
a group order of 777288435636813540 = 2^2*3*5*11*31*1823*38917*535489 thus:
1. In stage 1: B1 >= 535489 is required
2. Noting that 534241 is 44147th prime and 535489 the 44230th prime;
In stage 2: B1 >= 38917 is
"Brian J. Beesley" <[EMAIL PROTECTED]> wrote
- From [EMAIL PROTECTED] Sun Nov 10 20:22:33 2002
- On Saturday 09 November 2002 04:45, George Woltman wrote:
- > A harder problem is finding some smooth ECM curves to test. I do not
- > have tools to compute group orders. If someone can help by findi
On Saturday 09 November 2002 04:45, George Woltman wrote:
> A harder problem is finding some smooth ECM curves to test. I do not
> have tools to compute group orders. If someone can help by finding a
> couple of dozen smooth ECM test cases for exponents between 1000
> and 50, I would be most
On Saturday 09 November 2002 04:45, you wrote:
>
> A harder problem is finding some smooth ECM curves to test. I do not
> have tools to compute group orders.
Nor do I.
> If someone can help by finding a
> couple of dozen smooth ECM test cases for exponents between 1000
> and 50, I would be m
P-1 and ECM factoring is fairly complex code with several different
paths based upon how much memory is available. I'd like to develop a
fast QA suite for P-1 and ECM factoring. I intend to hardwire the test cases
into prime95 (or read the data from a QA file) so that I can run them with
several
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