20031203, 15:58  #1 
Jun 2003
3·5·107 Posts 
100 Most Wanted
I am interested in developing new factoring methods. In order to try these methods out I am looking for 100 candidates with different sizes having different size factors. If any one has any suggestions or has some candidates please post the numbers below. The problem working with some of the numbers that everyone is trying to factor is that they are hard to factor and an undeveloped method has little chance to factor them and hence we canโt figure out the power of the new factoring algorithm.
Citrix 
20031203, 16:23  #2  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2·7^{3}·17 Posts 
Re: 100 Most Wanted
Quote:
When you have something that seems to work on numbers of a particular size, then work on numbers of a similar size with unknown factorizations. If you don't want to practice beforehand, there are any number of tables of integers to be found. My web site at http://research.microsoft.com/~pleyl...ation/main.htm and links therein contains many thousands of such numbers. Paul 

20031203, 16:43  #3 
"William"
May 2003
Near Grandkid
2·1,187 Posts 
It's going to be hard to find numbers that people think of as "most wanted" but that haven't already had substantial attempts using ECM and perhaps P1 and P+1.
If suitable, I'd be glad to provide composite numbers from ElevenSmooth. The ECM Server for the ElevenSmooth project has 63 active composites. These range in size from 149 digits to 6936 digits. The C149 is presently testing for 50 digit factors (B1=43M). There are 22 numbers presently testing for 40 digit factors (B1=3M), ranging from 186 to 443 digits. The numbers between 490 and 1357 digits are being tested for 35 digit factors, the larger numbers are being tested for 30 digit factors. There are also about 100 composites that are presently being tested for 25 digit factors by the Special Project. The smallest of these are probably in the low 200 digits. I count the C149 as my "most wanted," but would be pleased to have factors for any of these. If any these meet your requirements, I'd be glad to provide the composites. 
20031203, 17:07  #4 
Jun 2003
1605_{10} Posts 
I could use these as a start and update the list as more people submit numbers. Post about 100 numbers below or PM them to me.
Thanks, Citrix 
20031204, 16:33  #5  
"William"
May 2003
Near Grandkid
2×1,187 Posts 
Quote:


20031212, 04:21  #6 
Sep 2002
2·331 Posts 
31074182404900437213507500358885679300373460228427
27545720161948823206440518081504556346829671723286 78243791627283803341547107310850191954852900733772 4822783525742386454014691736602477652346609 RSA 640 You could verify your factoring method works using the recently factored RSA 576 18819881292060796383869723946165043980716356337941 73827007633564229888597152346654853190606065047430 45317388011303396716199692321205734031879550656996 221305168759307650257059 
20031212, 06:56  #7  
Aug 2003
Upstate NY, USA
2·163 Posts 
Quote:


20031212, 14:32  #8  
"Sander"
Oct 2002
52.345322,5.52471
29·41 Posts 
Quote:


20031212, 14:53  #9  
Mar 2003
Braunschweig, Germany
E2_{16} Posts 
Quote:
Maybe US researchers even have to look for different factors of RSA576 to abide the law? 

20040112, 02:16  #10 
Jun 2003
3·5·107 Posts 
I am looking for all the factors of mersenne numbers under 2^2561.
that is 2^n1, n from 1 to 256 Could you please provide me with a website where I can download these numbers. Thanks, Citrix 
20040112, 03:12  #11 
Nov 2003
245_{8} Posts 
Although you have to write a program to reconstruct all factors for each number,The Cunningham Project Site should have everything you need.
Last fiddled with by nfortino on 20040112 at 03:12 
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