How much work on Odd Perfect Number search?

[jasong]

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 digit-level they represent, here.

(2) How the totwork number is defined:

assume you are referring to the ECMNet Client.

The output from the client should show the total number of curves done by the client for all numbers assigned by the server since the client started.

Here is the calculation for the work done for a single curve:

d_B1 * strlen(s_Number) * strlen(s_Number)/1000000000.

This is NOT accurate if s_Number is an expression instead of a decimal expansion of an expression. The "Total Work" calculation is (although slightly modified) is carried over from ECMNET 2.0k. You cannot use it to track curves you have done on a number or the total number of curves done for all clients on a number.

Edit: Maybe someone who does have an ecm client that tracks number of curves needed could post that information about once a week? Also, if your client happens to simultaneously print the 'work' number and total number of curves needed, it would be nice to know that.(My LInux and Windows clients seem to want to do one or the other, but not both.) Edit2: Maybe I'm wrong, but in the DOS window I have, there is something called 'Sum<B1>', I believe if you divide this number by 2000, you get the curves down at that digit level. The link earlier in this thread can tell you the total number of curves needed.

[jasong]

What I believe the Edit2 portion SHOULD say:

Edit2: Maybe I'm wrong, but in the DOS window I have, there is something called 'Sum<B1>', I believe if you divide your B1 value 1000, and then divide the 'Sum<B1>' by this new number, you get the curves down at that digit level. The link earlier in this thread can tell you the total number of curves needed.

[wblipp]

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.no-ip.com:8201

More Wanted Server:
http://oddperfect.no-ip.com:8202

Tiny Server
http://oddperfect.no-ip.com:8203

[jasong]

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?

[jasong]

Originally Posted by jasong

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 in OPN search? 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?

Bump for the above, quoted questions. Also, could someone print out a number to ecm(I mean print out what to type in)that would take about a half hour on an "average" machine, as well as how much "work" it is, as defined in the first post? I want to try to convince my team to run some curves.

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.

[wblipp]

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 (19^233-1)/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 time-per-curve 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^q-1)/(p-1) 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