20070517, 12:55  #1 
(loop (#_fork))
Feb 2006
Cambridge, England
2^{2}·1,613 Posts 
Have a look at the partition numbers
If you want the opportunity of running ECM 24/7 and getting a freshlybaked factor per CPU in your inbox most mornings, can I commend to you the partition numbers from
http://www.asahinet.or.jp/~KC2HMSM/mathland/part/ I am currently clearing up the 1300013500 range and running ECM on the 2000021000 range, but in other ranges there are literally thousands of numbers as small as C101 that have seen only ECM with B1=50k, and others that have been wellECMed and are just sitting there begging to be GNFSed. Come on in, fill your boots! There *are* interesting divisibility properties to be found among the partition numbers: the famous 5p(5n+4), 7p(7n+5), 11p(11n+6), and infinitely many (see http://www.sciencenews.org/articles/20050618/bob9.asp ) weirder ones (for example, part(17303n+237) is divisible by 13), but I'm fairly sure they don't apply for factors this big; on the other hand, there being no strong mathematical use for the factors is scarcely a disincentive for other factorisation projects. Trying to sound like an advocate for the Oregon Trail, Tom Last fiddled with by fivemack on 20070517 at 13:21 
20070517, 13:19  #2  
Nov 2003
2^{2}×5×373 Posts 
Quote:
Challenge contest back in the 90's. They were restricted to those with prime indices, but a VERY LARGE NUMBER of them were fully factored. Check the RSA website to see if the data is still available. I will check to see if I still have a copy of the data. Bob 

20070517, 13:36  #3  
(loop (#_fork))
Feb 2006
Cambridge, England
2^{2}·1,613 Posts 
Quote:


20070517, 14:17  #4  
Nov 2003
2^{2}×5×373 Posts 
Quote:


20070517, 15:34  #5 
Oct 2004
Austria
2×17×73 Posts 
Reserving 14984 c104 for msieve (QS)

20070517, 15:56  #6 
Banned
"Luigi"
Aug 2002
Team Italia
2×41×59 Posts 

20070517, 16:36  #7 
(loop (#_fork))
Feb 2006
Cambridge, England
2^{2}×1,613 Posts 
I don't think there are all that many people working on these numbers ... contributions this year have, with one exception, been by me or by Hisanori Mishima himself, which is really why I posted here to drum up more interest. It would be nice to tell him about the reservations, but he manages the site manually so we don't want to overload him entirely.

20070517, 16:39  #8 
(loop (#_fork))
Feb 2006
Cambridge, England
1100100110100_{2} Posts 
Out of curiosity, I collected all the cofactors together, and did 35 rounds of GCD(product of half the cofactors selected at random, product of the other half), all of which returned 1. So I think it's quite unlikely (IE there are about 2^24 pairs, and for any pair the probability is 2^34 that both were on the same side all 35 times) that any number will divide more than one of the cofactors.

20070517, 18:46  #9 
Oct 2004
Austria
2×17×73 Posts 
Reserving 29328 c101 and 28819 c102 (as an attempt to compare msieve's QS and GNFS with numbers in similar size)

20070517, 19:04  #10  
"Sander"
Oct 2002
52.345322,5.52471
29×41 Posts 
Quote:
I also has been a long time i did any numbers of the (Generalized) Cullen and Woodall numbers so i might return there first. 

20070517, 20:02  #11  
Jun 2005
lehigh.edu
2^{10} Posts 
Quote:
last quarter's prize. We quit when the prizes were no longer being given. But my recollection is that there was another round of factors waiting for the quarter to finish (to be eligible for the next quarter's prize), and that some of the later ones that we did submit never got included. I can check, but it has been quite some time. Again, we were only doing the ones of prime index (the thought being that there were too many of each given size, otherwise). Also, aside from the wish that there might be instances of new congruences/divisibilities found, these are (iirc) only gnfs candidates, with no chance of snfs  that was one of the appeals, in our case. Most of our early gnfs trials were taken from the partition list, the first ones for gnfs above c110, including c112, c119, c116 from our Crypto'95 paper on the cycle explosion (gnfs with four large primes). Bruce PS  sentance fragment patched. There are also some of our factors on one of Brent's early pages, from back when he was taking all ecm factors above p40 (especially the year or two when we were working toward p50, finished with Curry's p53). Last fiddled with by bdodson on 20070517 at 20:12 Reason: "memory rot"  cf. Thurston's version of "bit rot". 

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