ECPP - Scoring, or other primality tests (PFGW?)

[f1pokerspeed]

I am thinking of running Primo to get some certification work done for factorDB - the thing that is enticing me is the scoreboards based on the score ((n/1000)^4) where n is the number of digits. I am wondering - what kind of digit size would be the optimum for scoring the highest?

I have created an excel document with pre-filled formulae and some data collected from the ECPP website, however I am missing a lot of data. So, if someone could either fill in the data or give me a straight answer I would appreciate it.

(BTW: I am not lazy with the working of those sorts of numbers, I just simply don't have the time or money to run for days on end as an experiment).

If this may be too tedious for some, or you don't see my view on this (read the BTW) could you suggest another method (non-factorization, mind you) that I could contribute to the DB? (IE: Primality testing, but how would I go about doing it and submitting the results?)

The only way that I can think of for primality testing is PFGW or LLR, but how can I produce something like a certificate? Whenever I try and produce a certificate, the option is grayed out in the GUI. Does this mean I have to use the command line, or am I just plain missing something?

[schickel]

Originally Posted by f1pokerspeed

I am thinking of running Primo to get some certification work done for factorDB - the thing that is enticing me is the scoreboards based on the score ((n/1000)^4) where n is the number of digits. I am wondering - what kind of digit size would be the optimum for scoring the highest?

Short answer (and not intentionally snarky): run the largest numbers you feel comfortable running, obviously....

I have created an excel document with pre-filled formulae and some data collected from the ECPP website, however I am missing a lot of data. So, if someone could either fill in the data or give me a straight answer I would appreciate it.

Run time is going to depend on which version you're running, with hardware becoming a second-order effect, since the Linux multi-threaded version is so much vastly faster than the (last) Windows version.

(BTW: I am not lazy with the working of those sorts of numbers, I just simply don't have the time or money to run for days on end as an experiment).

Easy to understand that....sorry, though, I don't have any saved info right at hand to provide. (You could try looking for certs I ran above 3000 digits and digging the runtime out of them. Mine would be for a 4 or 6 thread run on an AMD 3GHz X6 [Running Ubuntu via VirtualBox].)

If this may be too tedious for some, or you don't see my view on this (read the BTW) could you suggest another method (non-factorization, mind you) that I could contribute to the DB? (IE: Primality testing, but how would I go about doing it and submitting the results?)

As of right now, those are the two primary contributions possible from outside the actual DB (factoring and primality proving).

If you figure that (S/G)NFS is too much, you can also run some ECM on some of the larger composites. a client/server setup would allow you to load more than one composite at a time with the added advantage of promoting compsoites as/when something cracks.

The only way that I can think of for primality testing is PFGW or LLR, but how can I produce something like a certificate? Whenever I try and produce a certificate, the option is grayed out in the GUI. Does this mean I have to use the command line, or am I just plain missing something?

As far as primality proving, Primo is the only way to go right now. The certificates are only Primo certificates (so far). (N+/-1 proofs are also possible, with Primo certification of helper primes being one way to achieve larger proofs via running smaller numbers through Primo, but the smaller Primo certs are the only ones that "count" on the leaderboard.)

[wblipp]

Originally Posted by f1pokerspeed

could you suggest another method (non-factorization, mind you) that I could contribute to the DB?

I have a little project ready to go that you might want to take over. It will generate N-1 primality proofs for some numbers of some interest to the Odd Perfect project. These arise like this:

let p, q, s, a, and b be primes with

b= -1 mod a

q = (p^b-1)/(b-1)

s = ((q^a-1)/(q-1))/((p^a+1)/(p+1))

Then s-1 has a factor of (p^b-1)/(p-1)+p. With a little luck, this may factor s-1 sufficiently to complete the N-1 proof.

For example, for a=7 b=13 p=206081

q is this 64 digit prime

s is this 351 digit prime

supplying the algebraic factor of s-1 was enough to get it fully factored, allowing the primality proof. I have about 90 of these with s ranging from 304 to 692 digits. I'll be glad to make the list available to you or anybody else that wants to do this. If nobody else is interested, I'll do it myself sometime in next week.

William

[xilman]

Originally Posted by wblipp

I have a little project ready to go that you might want to take over. It will generate N-1 primality proofs for some numbers of some interest to the Odd Perfect project. These arise like this:

let p, q, s, a, and b be primes with

b= -1 mod a

q = (p^b-1)/(b-1)

s = ((q^a-1)/(q-1))/((p^a+1)/(p+1))

Then s-1 has a factor of (p^b-1)/(p-1)+p. With a little luck, this may factor s-1 sufficiently to complete the N-1 proof.

For example, for a=7 b=13 p=206081

q is this 64 digit prime

s is this 351 digit prime

supplying the algebraic factor of s-1 was enough to get it fully factored, allowing the primality proof. I have about 90 of these with s ranging from 304 to 692 digits. I'll be glad to make the list available to you or anybody else that wants to do this. If nobody else is interested, I'll do it myself sometime in next week.

William

I'm being particularly dim today. As I read your message, all you want to do is for someone to evaluate (p^b-1)/(p-1)+p where the values of p and b are given by you. I must have misunderstood because that activity is so utterly trivial that you would have spent less effort doing it than posting about it.

What do you actually want a prospective contributor to do? Find a currently unknown factor of a list of 90 values for composite 's' or something else?

Paul

[f1pokerspeed]

Originally Posted by wblipp

I have a little project ready to go that you might want to take over. It will generate N-1 primality proofs for some numbers of some interest to the Odd Perfect project.

<snip>

supplying the algebraic factor of s-1 was enough to get it fully factored, allowing the primality proof. I have about 90 of these with s ranging from 304 to 692 digits. I'll be glad to make the list available to you or anybody else that wants to do this. If nobody else is interested, I'll do it myself sometime in next week.

William

Is there a program to do this or do i have to manually plug in the numbers? Also, timescale for it? Minutes, days?

[wblipp]

Originally Posted by xilman

What do you actually want a prospective contributor to do?

It's a trivial activity. Most of the time is actually spent clicking the buttons to kick off a primality test. I'll confess that I get a lot of fun out of seeing those primality proofs come together, and I may not be the only one.

But you're right that it is trivial. I wouldn't have even mentioned it except that f1pokerspeed was looking for something to do with the factordb that didn't involve factoring, and I happened to be finishing up the process of gathering the currently interesting examples of this.

William

[wblipp]

Originally Posted by f1pokerspeed

Is there a program to do this or do i have to manually plug in the numbers? Also, timescale for it? Minutes, days?

If I do it myself, I will use a spreadsheet to build factoring facts of the form

"s-1 = (p^b-1)/(p-1)+p"

as text strings from p,a,b, then submit them to the Report Factors page. The build another set of strings of the form

"s=1"

and do it again. The second set will get the primes into the factordb and will return a page with a link to each of them. Then I'll step through s values, clicking on "open in new tab," "Primality," "Proof" or "N-1." Displaying N-1 might find a few more more factors, allowing "Proof" the next time.

A slightly less trivial project would be to see if minor ECM will complete proofs that are not automatic.

An hour or so should exhaust all the automatic possibilities. ECM until bored.

[f1pokerspeed]

So, would it be possible to just create some ECM work and distribute some of it then?

I could take some of the workload as I have some spare time.

[xilman]

Originally Posted by wblipp

If I do it myself, I will use a spreadsheet to build factoring facts of the form

"s-1 = (p^b-1)/(p-1)+p"

as text strings from p,a,b, then submit them to the Report Factors page. The build another set of strings of the form

"s=1"

and do it again. The second set will get the primes into the factordb and will return a page with a link to each of them. Then I'll step through s values, clicking on "open in new tab," "Primality," "Proof" or "N-1." Displaying N-1 might find a few more more factors, allowing "Proof" the next time.

A slightly less trivial project would be to see if minor ECM will complete proofs that are not automatic.

An hour or so should exhaust all the automatic possibilities. ECM until bored.

I'm a bear of very little brain and I'm having difficulty working out what you would like to be done

if/when you and your cow-orkers get your act together, please send me a list of composites and an estimate of how much ECM work has been done. I'll see what can be found.

[Dubslow]

Originally Posted by xilman

I'm a bear of very little brain and I'm having difficulty working out what you would like to be done

All too easy (Perhaps you are not as strong as...)

PS Little brain indeed

[schickel]

Originally Posted by f1pokerspeed

So, would it be possible to just create some ECM work and distribute some of it then?

I could take some of the workload as I have some spare time.

As noted, a client/server setup would be the easiest to administer.

You can even set it up on one computer. The client in this case would just use the localhost connection to talk to the server, but this setup would allow multiple composites to be loaded into the server to allow for numbers to be ready on standby should something factor.

I set mine up on my home network to allow me to use all my local machines to do ECM work when I don't have them doing something else.

To get started with this kind of thing, go to rogue's site and download one of the ECMNet packages. (v3.0.2 will require the installation of a DB backend to work, but the earlier version will not.) After setup, just get some composites of a suitable size and load them into the server and start it up. The "best" initial size would be impossible to guess, since the amount of ECM already done would be unknown, except for numbers from the more well-known projects, but certainly 200-300 digits would be a good starting point until you know how fast/many curves you can run (smaller would work also, but anything below ~140 or so would probably be better attacked with NFS).

I can help getting the earlier version up and running, since that's what I'm using, and I'm sure there are others here that could assist you with v3.