20031203, 20:16  #1 
Nov 2003
1D24_{16} Posts 
Hi,
With so many other projects already running, this one seems pointless. What is special about the number you are trying to factor, and what do you hope to accomplish? If you want to factor numbers of the form 2^n1, there are many smaller candidates. A worthwhile event would be to FINISH the Cunningham base 2 tables. AFAIK, it is the longest ongoing computational project in history. Bob 
20031204, 03:19  #2 
"William"
May 2003
New Haven
2361_{10} Posts 
Hello Bob,
Welcome to ElevenSmooth. Perhaps you don’t understand how algebraic factors work for highly composite exponents like 3326400. We have already found factors of 2^14851 and 2^15751, themselves algebraic factors of 2^33264001. You can see all our results for small exponents by sorting our Factors Page by clicking on the header for Mersenne. Sam Wagstaff, the present keeper of the Cunningham Project, defines it as ”seeks to factor the numbers b^n + 1 for b = 2, 3, 5, 6, 7, 10, 11, 12, up to high powers n.”. The history of the Cunningham Tables has been to extend the base 2 tables in every edition. So ElevenSmooth is already part of the Cunningham Project, and the Cunningham Tables will grow into our factors. I assume your questions were rhetorical, but I have explained what attracted me to M(3326400) in the FAQ Question Why 3326400?. You might also be interested in the FAQ Question about Primitive Parts. You sound like our kind of guy – somebody who believes that people should be working on the Cunningham Project. Why not go to our Download Page and get started? William 
20031204, 04:42  #3 
Sep 2003
13·199 Posts 
Are you "the" Bob Silverman?
Any ideas for projects? People are certainly free to propose and organize their own small projects... I imagine that if the new Mersenne prime exponent had had a suitable residue modulo 8, we might have seen a small project organized to find new primitive trinomials with it (Richard Brent's project). Many of us just stick to 2^{P}1 though. 
20031204, 11:45  #4  
Bamboozled!
"𒉺𒌌𒇷𒆷𒀭"
May 2003
Down not across
10643_{10} Posts 
Quote:
I thought he just proposed a project: clearing out the Cunningham base 2 tables. Paul P.S. Hi Bob. I didn't know you were here too. 

20031204, 17:32  #5 
Nov 2003
2^{2}×5×373 Posts 
Wblipp wrote:
"Hello Bob, Welcome to ElevenSmooth. Perhaps you don’t understand how algebraic factors work for highly composite exponents like 3326400. " ROTFL. Do you have any idea who I am? Any time the range of a factoring table is extended. it becomes EASY to find a lot of factors. Finishing off 2^n1 and 2^n+1 for n <= 1200 is CHALLENGING. Furthermore, we actually learn something about the algorithms in the process. NFS requires a lot of parameters. We do not know how to select them for a 1024bit number currently. But gradually pushing NFS at larger and larger numbers gives us useful information. Just throwing someone else's existing ECM code at an extension of a table takes the I.Q. of a peanut. (no personal offense intended; I am not denigrating your work, just suggesting that there are better uses for the CPU time). Please explain the purpose of factoring 2^3326400 1 . What will you find out? How will you improve algorithms? You are not even pushing the limits of ECM. Looking for 25 to 40 digit factors is EASY. Bob 
20031204, 19:09  #6  
Aug 2002
Buenos Aires, Argentina
5×269 Posts 
Quote:
But when we try to factor greater numbers it is much more difficult to use ECM. How much time do you need to find a factor of about 40 digits of the primitive part of M(3326400)? Beyond this limit it is certanly easier to find some factors of the composite number by trial division than by ECM. Another example of factorizations of huge numbers is my page of prime factors of numbers near googolplex. How do you use another method other than trial division in order to find factors of these numbers? As you can see, maths does not end with numbers of about 400 digits. There are other challenges out there. 

20031204, 20:02  #7  
"William"
May 2003
New Haven
3·787 Posts 
Quote:
Quote:
Somebody has to sweep the floor  to come along and do the things that are easy but haven't yet been done. Sweeping the floor, as you say, takes only the brain of a peanut. Even so, clean floors are desirable. My abilities and interests run towards sweeping this floor, and I know from personal experience that these easy results are ocassionally of interest. William the PeanutBrained 

20031204, 23:32  #8  
Sep 2003
2587_{10} Posts 
Quote:
I meant some ideas for an entirely new project idea, something small but doable by say a few dozen computers... this board is probably the place where such projects can be proposed and draw a few interested folks, much like the already existing ones in the "Other Projects" subsection. 

20031205, 00:03  #9  
Jun 2003
The Texas Hill Country
3^{2}·11^{2} Posts 
Quote:
However, in the case of "Eleven Smooth", the "value" has not been adequately explained to satisify Bob (or myself). I think that Bob is simply asking you to outline the goal and compare that goal to alternate efforts. Why should we expend our effort on your project instead of .....? 

20031205, 00:18  #10  
Sep 2003
13·199 Posts 
Quote:
Quote:


20031205, 04:15  #11  
Sep 2003
5033_{8} Posts 
Quote:
If you reply, perhaps it could be in that thread rather than this one. 

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