20030808, 06:33  #1 
Jun 2003
40_{16} Posts 
Post the numbers you have tried to factor here
Post the numbers you have tried to factor (without success) and how much work you have done here. Maybe someone will go on with your numberFor example, maybe me :)

20030808, 11:41  #2  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
10110010011110_{2} Posts 
Re: Post the numbers you have tried to factor here
Quote:
To get the ball rolling, I'm currently working on generalized Cullen and Woodall numbers. All have had ECM run to 25 digits. and some a little more. There are 14067 unfactored composites, which is why I post the URL http://research.microsoft.com/~pleyl...oodall/gcw.htm rather than the numbers themselves. You will find other integers I'm interested in on links within http://research.microsoft.com/~pleyl...ation/main.htm Paul Last fiddled with by smh on 20031018 at 22:45 

20030808, 13:25  #3 
"Mark"
Apr 2003
Between here and the
3×17×131 Posts 
I have been working on Home Primes at Sander Hoogendoorn's website at http://home.zonnet.nl/sander.hoogend...oendprime.html for a long time, but have been stuck for months without finding a new factor. There is the possibility that I broke GMP because I had been coding and testing some improvements to mpn routines earlier this year, but I'm fairly certain that I removed those changes and rebuilt the library before resuming my search. Of course I could just be unlucky as most of the composites are over 110 digits and have had enough ECM curves to find factors up to 40 digits. HP(49) has not been found yet. The current composite is 204 digits. More info can be found at http://www.worldofnumbers.com/em_topic1.htm.

20030808, 18:49  #4 
"Sander"
Oct 2002
52.345322,5.52471
29×41 Posts 
Hi Mark,
I missed the progress on HP(49). It happened while i was away for holidays. I'll try to update asap, but yesterday i reinstalled my computer (new disk) and haven't restored any of the data yet, so it might take a couple of days. To be honest, i haven't done any ECM on these numbers lately. I might consider doing some 3M curves on that C204. Before my holidays i did factor quite a few numbers with SNFS from Paul's site. At the moment i don't have a pc available in the office to run long snfs runs, and at home it's to hot currentely to keep my pc running for hours. Only helping Wblipp with some ECM at the moment. 
20030808, 22:15  #5 
Feb 2003
2·3·29 Posts 
I have done a fair amount of work over the past few years on various Fermat numbers (status page), but to no avail. I gave up on them and started a LMH range instead, but I'll probably go back eventually. :)

20030809, 18:33  #6 
Aug 2002
Buenos Aires, Argentina
2×727 Posts 
I'm factoring numbers near a googolplex using trial division. A googolplex is a one followed by a googol zeros, i.e., 10^100 zeros.
You can find the results at: http://www.alpertron.com.ar/GOOGOL.HTM (googolplex to googolplex+999) and http://www.alpertron.com.ar/GOOGOLM.HTM (googolplex999 to googolplex) 
20030810, 01:57  #7 
"Mark"
Apr 2003
Between here and the
3·17·131 Posts 
Unfortunately I don't have SNFS or source code to build it. I don't know if it is x86 specific or can be compiled on ther CPUs. I also don't know what resources are required to run it (lots of GHz hours, etc.?). Does anyone have a link to source code for SNFS?
The main reason I like Sander's project is that it is small and probably finite in size, although that is unknown. Granted one could expand to higher numbers to find home primes, but at this time I don't know if a home prime will be found for each value < 1000. I like the idea of knocking a few more off the list. I also like the idea that most of the remaining composites should have primes factors over 45 digits, but small enough to be found with ECM, thus getting the person who finds such a factor into Richard Brent's Top 100 ECM factors table. BTW, another interesting factoring project is at http://www.fermatsearch.org. It doesn't use ECM but a prebuilt Windows client is available and [selfish plug] a compileityourself client that uses GMP is also available for other CPUs [/selfish plug]. The nice thing about this project is that you get a little more notoriety for finding a new factor of a Fermat number. As for Paul Leyland's GC/GW factorization, its will take many years to factor all of those numbers and that most likely will not happen in my lifetime. Perhaps more algebraic factorizations can be found that could shorten his list significantly. What I do like about his project is that with so many candidates, it shouldn't be difficult to find a composite with B1=1e6. I can't speak for P+1 or P1 factoring. I know that I tried hundreds of his composites with P1/P+1 and B1=1e6 with no luck. I assume that someone else might have done that work. Of course things would change if a quantum computer of sufficient size became reality, which seems to be possible with the direction of today's technology. But if that happens, ECM/QS/NFS factoring would become passe quickly. Mark 
20030813, 09:40  #8 
Aug 2003
Europe
2×97 Posts 
I have also got a little factorization effort here.
http://people.zeelandnet.nl/flaters/gmpecm.htm It tries to factor Lucas numbers with GMPECM methods. ALtho the server it self is still wel not behind a decent router and the client doesn't support proxies to goodly. But ok. There is source and prebuilt downloads available.. ANd stats are being maintaind but still need to write a decent front for it so that is why it is not visable for now. Current Lucas GMPECM server runs at 217.19.25.214 at ports 23, 80 and 110 So if you are intressted and or tempted to try it out ;) be my guest. 
20030813, 13:14  #9  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2×5,711 Posts 
Quote:
If you want to run ECM, I recommend starting at B1=44M and to confer with Alex so that you keep each other informed on progress. Paul Last fiddled with by smh on 20031018 at 22:47 

20031118, 05:32  #10 
Bemusing Prompter
"Danny"
Dec 2002
California
2^{3}×3×103 Posts 
RSA numbers.

20031119, 05:35  #11 
Sep 2002
Vienna, Austria
3×73 Posts 
Prelimitive part of 460^800+1.
The number have 4 small prime factor and a c1687. I've only tried 30 curves with B1=2k without success. 
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