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View Poll Results: A new subforum dedicated to Fermat factorization?
Yes, great! 8 34.78%
Hm... why not? 4 17.39%
Dunno. 5 21.74%
Useless... 6 26.09%
Voters: 23. You may not vote on this poll

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Old 2010-03-28, 22:43   #1
ET_
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Default Fermat factorization subforum poll

I think a new subforum dedicated to Fermat factorization would be great. Just think about:

- ECM management
- Algorithms discussion
- Software development
- Heuristics
- Correlation among different factorization systems
- History
- Hints on use of different software

Last fiddled with by ET_ on 2010-03-28 at 22:50 Reason: Added some reasons to vote...
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Old 2010-03-28, 23:15   #2
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... Links to pages of current/summary status
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Old 2010-03-28, 23:47   #3
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... GFN factorisation too?
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Old 2010-03-28, 23:53   #4
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Recent successes notwithstanding, I suspect such a subforum would be pretty quiet. Almost all the issues above relating to further research and optimum program usage apply to factoring other numbers.

How about a sticky in the factoring format that can provide links to related web pages and pointers to the occasional ECM success threads?
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Old 2010-03-29, 04:47   #5
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I agree with George that a sticky thread would be more useful than a subforum. One thing that is missing that was available on the old pages is a summary of P-1 limits on Fermat numbers. As Ernst has pointed out, P-1 might have discovered the most recent factor of F22 had it been pushed far enough.
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Old 2010-03-29, 08:16   #6
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Quote:
Originally Posted by Prime95 View Post
Recent successes notwithstanding, I suspect such a subforum would be pretty quiet. Almost all the issues above relating to further research and optimum program usage apply to factoring other numbers.

How about a sticky in the factoring format that can provide links to related web pages and pointers to the occasional ECM success threads?
I agree with you, a sticky thread may be enough to collect information.

I remember a bunch of messages written by Ernst, Phil and Mike and related to this subject that I would like to see in the Fermat sticky thread: ECM curves comparison between Prime95 and GMP-ECM, tables about memory allocation and a few ideas about sieving large ranges.

I also would like to start talking about porting GMP-ECM under CUDA after Oliver (a.k.a. TheJudger) completes his GPU-aware Mersenne factorization applet.

And I feel the need to port FermFact program under 64 bit (or Linux at least), or ask Geoff instructions on how to implement a similar sieve.

I exchanged messages with Wilfrid Keller, and he felt a bit puzzled noting that there is little coordination on the ECM side of Fermat factorization.
Now, with the new version of PrimeNet, things are getting better, but there are still users that don't (or don't care to) report their (often manual) curves to GIMPS.

I don't explicitly ask for a subforum: a sticky thread may suffice, but there is really much to talk about IMHO.

Luigi

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Old 2010-03-29, 15:47   #7
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Hi,
I'm not really a math freak and don't know much about all the different numbers to factorize and the alg. behind. To make it much easier to contribute to Fermat factorization I would like to see a page with all remaining composites (not only C223232, but the real value) and how many ecm curves were already done for different B1 and how many are left.
yoyo
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Old 2010-03-29, 16:12   #8
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Quote:
Originally Posted by yoyo View Post
Hi,
I'm not really a math freak and don't know much about all the different numbers to factorize and the alg. behind. To make it much easier to contribute to Fermat factorization I would like to see a page with all remaining composites (not only C223232, but the real value) and how many ecm curves were already done for different B1 and how many are left.
yoyo
The real values for C223232 etc are easily calculated by looking at the known factors in www.prothsearch.net/fermat.html. I don't know if there is a place where they are written explicitly.

The leading edge of ECM factoring that is reported to PrimeNet is, in my opinion, well presented at www.mersenne.org/report_ECM/. As Luigi said: the problem is that not all effort is reported to PrimeNet-server. The page is showing only the status of the current bounds that are assigned by the server, but that should be enough for most purposes.

The trial factoring ranges for larger Fermat numbers are in my opinion also adequately presented at www.fermatsearch.org.


On the original question about the need for a subforum: I don't think there is (yet) a need for it. I mean, we are probably not getting 2 factors a month from this point on (or are we? ) A sticky with the recent history and links to all the relevant forum-threads (and to sites like the ones mentioned in this post) would be perfect.

Last fiddled with by rajula on 2010-03-29 at 16:13
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Old 2010-03-29, 17:32   #9
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Quote:
Originally Posted by yoyo View Post
Hi,
I'm not really a math freak and don't know much about all the different numbers to factorize and the alg. behind. To make it much easier to contribute to Fermat factorization I would like to see a page with all remaining composites (not only C223232, but the real value) and how many ecm curves were already done for different B1 and how many are left.
yoyo
If you would like to see such a page, why don't you create one?

Paul
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Old 2010-05-06, 15:53   #10
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The poll is clsoed...

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Old 2010-07-09, 13:45   #11
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Quote:
Originally Posted by yoyo View Post
Hi,
I'm not really a math freak and don't know much about all the different numbers to factorize and the alg. behind. To make it much easier to contribute to Fermat factorization I would like to see a page with all remaining composites (not only C223232, but the real value) and how many ecm curves were already done for different B1 and how many are left.
yoyo
It would be very sensible to list all remaining composites, but there are also other questions which do not seem to have been raised in the mathematics world.

One that has especially interested me for lack of interest is the cofactor of F25. F25 already has three prime factors known, but the most recently found was discovered as long ago as 1987. What surprises me is that no effort seems to have been made to prove the cofactor of F25 as composite, though F24 was proven composite as early as 1999. I know from having read about Fermat numbers for years that it is extraordinarily improbable that the cofactor of F25 would be found to be a probable prime, and totally impossible given that F25 has over ten million digits (I am not sure how many exactly) that it could be proven if it were a probable prime.

Another thing that could be discussed on a Fermat subforum is factors of generalised Fermat numbers. I know of tables of these for bases 6, 10 and 12 with full factorisations as known to date.

The most wanted number here is F9(10) or 10512+1. F9(10), though smaller than the ordinary Fermat number F11, has not been completely factored twenty-two years after F11 was factored in 1988. It is known that F9(10) has at least five prime factors, and that:
Code:
  • F9(10) = 1514497 Β· 302078977 Β· 3611707318387778163302401 Β· [60519945959443763729111699457765126549264698292851421880385435858790152813545290924845506386542387155941985421219244024954303660186678855842303923192009857497948485231312969155745835453746165321469423904826146527794046820875696222139256661621526103070954414073399792885257457060873994647522031459730135221392060573923764668121490089709489240538340002424066549724301935932502877840716671365418187024067731435117126707706102066639951386475089628375114985088101487681968252929]
I wonder how much work in being done on the factorisation of F9(10) into primes. Of the known factors of F9(10), the first was found in 1969, the second in 1992 and the third in 2000. I am not even sure what the limit of testing for F9(10) is - could anyone tell me?

Last fiddled with by xilman on 2010-07-09 at 15:26 Reason: Add [ code] tags for ease of reading.
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