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 2003-12-03, 20:16 #1 R.D. Silverman     Nov 2003 1D2416 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^n-1, 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
 2003-12-04, 03:19 #2 wblipp     "William" May 2003 New Haven 236110 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 2^1485-1 and 2^1575-1, themselves algebraic factors of 2^3326400-1. 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
 2003-12-04, 04:42 #3 GP2     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 2P-1 though.
2003-12-04, 11:45   #4
xilman
Bamboozled!

"𒉺𒌌𒇷𒆷𒀭"
May 2003
Down not across

1064310 Posts

Quote:
 Originally posted by GP2 Are you "the" Bob Silverman? Any ideas for projects?
No, he's just a Bob Silverman. Didn't you know they came in six-packs? (Apologies to Douglas Adams.)

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.

 2003-12-04, 17:32 #5 R.D. Silverman     Nov 2003 22×5×373 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^n-1 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 1024-bit 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
2003-12-04, 19:09   #6
alpertron

Aug 2002
Buenos Aires, Argentina

5×269 Posts

Quote:
 Originally posted by Bob Silverman Any time the range of a factoring table is extended. it becomes EASY to find a lot of factors. Finishing off 2^n-1 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 1024-bit number currently. But gradually pushing NFS at larger and larger numbers gives us useful information. [....] 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 [/B]
It appears that in the range you are suggesting ECM finds easily the factors in the range 25 to 40 digits. Even my applet written in Java was able to find a 44-digit factor and helped to find many factors of partition numbers.

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.

2003-12-04, 20:02   #7
wblipp

"William"
May 2003
New Haven

3·787 Posts

Quote:
 Originally posted by Bob Silverman Do you have any idea who I am?
I'm aware of a Robert D. Silverman who is credited extensively in the Third Edition of the Cunningham book. I guessed you were not that person because I thought that Silverman would have been surer that the Cunningham Project was the longest collaborative computing effort.

Quote:
 Originally posted by Bob Silverman 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.
Many of the factors we've found are MUCH smaller than 25 digits. Nine of them are only 11 digits long. When I was constructing partial coverings for Sierpinski candidates to make estimates for SeventeenOrBust, these are the numbers I wanted. Thanks to Will Edgington, there is a method to distribute these factors to anyone who cares, and thanks to many other people, these factors are well within reach. But "EASY" and "DONE" are not the same thing.

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

2003-12-04, 23:32   #8
GP2

Sep 2003

258710 Posts

Quote:
 Originally posted by xilman I thought he just proposed a project: clearing out the Cunningham base 2 tables.
I thought that one was already ongoing :)

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.

2003-12-05, 00:03   #9
Wacky

Jun 2003
The Texas Hill Country

32·112 Posts

Quote:
 Please explain the purpose of factoring 2^3326400 -1 .
I think that Bob's point was that he fails to see how this effort actually advances "knowledge". Those of us who have been factoring for many years realize that finding factors of "only" 30 or 40 digits is not difficult, in terms of the current state of the art. But expending ANY effort to do so should be justified by the value obtained in doing so. For example, if the number is one of the few remaining is some series, it is certainly worthwhile to find any "small" factors before embarking on an expensive effort to find the remaining factors by methods such as NFS. As a case in point, we spent a month or two examining M811 by ECM before committing 100 GHz-years to factoring it by NFS.

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 .....?

2003-12-05, 00:18   #10
GP2

Sep 2003

13·199 Posts

Quote:
 Originally posted by GP2 I thought that one was already ongoing :) 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.
For instance, almost five years ago "some guy" posted this to sci.math:

Quote:
 I have done numerical work on the pi(x) conjecture. i.e. pi(a + b) < pi(a) + pi(b) Work of Hensley & Richards showed it is incompatible with the prime k-tuples conjecture and that if we designate b as the smaller of a,b, then if a counter example exists then b < 2000. My numerical work has shown b > 750 for a counter example. This problem is within computer reach. I don't have the CPU resources anymore to continue with it. http://groups.google.com/groups?as_u...com%3E%231%2F1

2003-12-05, 04:15   #11
GP2

Sep 2003

50338 Posts

Quote:
 Originally posted by GP2 For instance, almost five years ago "some guy" posted this to sci.math:
Just a clarification. By amazing coincidence I actually posted about this very topic back in September in the Math forum (http://www.mersenneforum.org/showthr...&threadid=1080) and would be genuinely interested to know if you still think such a project is computationally "within reach" (especially with 5 years of Moore's law since those words were written).

If you reply, perhaps it could be in that thread rather than this one.

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