20070121, 01:23  #1  
"Jason Goatcher"
Mar 2005
DB3_{16} Posts 
How much work on Odd Perfect Number search?
For the sake of those involved in the ecm aspect of the OPN search on Windows computers, I politely supply the following information:
(1) There is a webpage that lists ecm parameters and tells what digitlevel they represent, here. (2) How the totwork number is defined: Quote:
Last fiddled with by jasong on 20070121 at 02:17 

20070121, 02:35  #2  
"Jason Goatcher"
Mar 2005
3·7·167 Posts 
What I believe the Edit2 portion SHOULD say:
Quote:


20070121, 03:27  #3 
"William"
May 2003
New Haven
3×787 Posts 
The ECM Server provides an html report of status. The three servers have the same numbers, but have different numbers active.
Most Wanted Server: http://oddperfect.noip.com:8201 More Wanted Server: http://oddperfect.noip.com:8202 Tiny Server http://oddperfect.noip.com:8203 
20070121, 03:31  #4 
"Jason Goatcher"
Mar 2005
3×7×167 Posts 
Thanks, I never realized this was available.
Btw, is there a way to use the 'work' value that the program ecmclient supplies to calculate how much work is necessary to get to the next digit level? Assuming, of course, no factor is found. Also, still assuming no factor is found with ecm, is there a curve point goal where it will be time to look for alternate methods? Last fiddled with by jasong on 20070121 at 03:40 
20070410, 23:28  #5  
"Jason Goatcher"
Mar 2005
3×7×167 Posts 
Quote:
To wblipp: Since it's your project I'm interested in getting my friends to help, please pick a good number on the Most Wanted server, and, if you would(for benchmarking purposes): PM the name of the composite, the actual number, and where it needs to be before advancing on to other methods. I would prefer that finding a factor advances the lower bound(or finds an OPN ) If I can convince my friends to run this project, it would be great if port 8204 could be JUST that one number. But don't do that just yet, my "rallying of the troops" might not accomplish anything. 

20070411, 03:00  #6 
"William"
May 2003
New Haven
3×787 Posts 
It's my desire to get this project to the point where it's easy to respond to a request like yours. This project naturally permits focused efforts in one region that contibute to other efforts. Unfortunately, my overload work situation has continued far beyond my expectation, and I do not have in place the infrastructure to make a really good response.
If I had a "proof generation" program, it would spit out numbers for which factors are needed. These would mostly not exceed 125 digits and would be great choices  but I don't have that program. Until that time, I see four tasks that might meet your needs. 1. You could pick up (19^2331)/18 from the most wanted list. There are several smaller roadblocks, but this one needs more ECM curves at B1=11M, which fits into your timepercurve limit. A factor would be useful even if we don't find factors for the smaller roadblocks because we will eventually create special case arguments for those that we don't factor. 2. Most of the numbers in the "More Wanted" ECM Server have no known factors. Many of these are eventual roadblocks because they are capstones of factor chains with no known additional factors. These limits are mostly far beyond the limits of the Most Wanted numbers, though. 3. You could pick your personal "base" prime "p" and look for factors of (p^q1)/(p1) for primes "q" for as far as you have interest and stamina. Enough of these factors would make it possible to construct a proof that any OPN divisible by "p" must exceed 10^n. These lemmas get piled together in proving any OPN must exceed 10^n. There are some bases that have been used by other OPN researchers that have not received a lot of attention yet. 4. I have many composites between 80 and 140 digits that are not really necessary, but are small enough to be easily factored with GNFS or SNFS. Most of these numbers, especially above 100 digits or so, should have more ecm work done first. You could undertake the "qualification" of these numbers, with the unfactored ones graduating to the "composites" page for NFS factorization. Let me know if any of these choices are attractive. William 
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