[QUOTE=lorgix;238235]I'm guessing database size is a problem.[/QUOTE]

I don't know whether database size is a problem. I imagine it's just that recording and coordination beyond the minimum necessary to find primes has been developed in a rather [I]ad hoc[/I] fashion.

I have a concrete example of what I've been talking about: M106391. This number has a 58 bit factor almost certainly discovered long ago by TF. The cofactor, according to [URL=http://www.garlic.com/~wedgingt/factoredM.txt]Eddington's list[/URL] "is at least a pseudo-prime in some base other than 2" according to his [URL=http://www.garlic.com/~wedgingt/mersfmt.txt]explanation of the codes[/URL]. Yet someone has done 15 curves on it.

Instead of ECM, further work on this exponent should focus on strengthening its probable prime status, (alternatively, proving that it is in fact composite, whereupon ECM could resume), in preparation for a future primality proof. At over 32,000 digits, a proof is probably unfeasible currently, but it may be reachable with a few years.

[QUOTE=lorgix;235452] But once a number is declared composite (by testing or factoring) the following efforts to factor it can often times be described as a scrambled mess.

I can think of several ways to go about this... One could assign the task that is most likely to yield a new factor, given the hardware and time at hand. ... One could also allow users to choose to concentrate their efforts to a range or a single number, optimizing parameters given conditions like hardware etc. We might also be able to combine P-1 and ECM efforts better. And avoid the same P-1 being done several times.[/QUOTE]

IMHO I think GIMPS does a pretty good job on pre and post factoring - that is, when you allow the server to manage assignments.
1. TF to the recommended number of bits -1
2. P-1 with calculated parameters
3. Last bit of TF
4. ECM systematically.

Now, because this is an open volunteer participation project is actually quite easy for any of us to "choose" work assignments differently. Right or wrong, I am among the list of people who have done so more for personal reasons than purely what is best for GIMPS.

Some examples:
- M1061 to 62 bits has been TF'd well beyond recommended parms because someone thought/hoped/wished that maybe the factor is just one bit higher. But being the lowest composite not yet factored there is a lot of strong interest is being the one to factor it.
- When you see an exponent P1'd many times (1000003) it is simply a case of someone not fully understanding how P1 works; that subsequent P1s with slightly higher parms have a VERY SMALL chance of succeeding.

But notice that, other than possibly pointing this out to them, NO ONE is going to stop you from working on whatever you so choose.

[QUOTE=petrw1;238268]IMHO I think GIMPS does a pretty good job on pre and post factoring - that is, when you allow the server to manage assignments.
1. TF to the recommended number of bits -1
2. P-1 with calculated parameters
3. Last bit of TF
4. ECM systematically.

Now, because this is an open volunteer participation project is actually quite easy for any of us to "choose" work assignments differently. Right or wrong, I am among the list of people who have done so more for personal reasons than purely what is best for GIMPS.

Some examples:
- M1061 to 62 bits has been TF'd well beyond recommended parms because someone thought/hoped/wished that maybe the factor is just one bit higher. But being the lowest composite not yet factored there is a lot of strong interest is being the one to factor it.
- When you see an exponent P1'd many times (1000003) it is simply a case of someone not fully understanding how P1 works; that subsequent P1s with slightly higher parms have a VERY SMALL chance of succeeding.

But notice that, other than possibly pointing this out to them, NO ONE is going to stop you from working on whatever you so choose.[/QUOTE]

GIMPS does a good job, no doubt.

But for factoring other than ECM; a little more record keeping would be nice.

I can understand that it might not have the highest priority though.

[QUOTE=Mr. P-1;238257]I have a concrete example of what I've been talking about: M106391. This number has a 58 bit factor almost certainly discovered long ago by TF. The cofactor, according to [URL=http://www.garlic.com/~wedgingt/factoredM.txt]Eddington's list[/URL] "is at least a pseudo-prime in some base other than 2"[/QUOTE]

For what it's worth, I've just calculated (using PFGW) that this number is a 3-PRP and a 7-PRP.

[QUOTE=Mini-Geek;238270]For what it's worth, I've just calculated (using PFGW) that this number is a 3-PRP and a 7-PRP.[/QUOTE]

Also 13-PRP, 17-PRP and 31-PRP.

[QUOTE=petrw1;238268]IMHO I think GIMPS does a pretty good job on pre and post factoring - that is, when you allow the server to manage assignments.
1. TF to the recommended number of bits -1
2. P-1 with calculated parameters
3. Last bit of TF
4. ECM systematically.[/QUOTE]

This is only the case with exponents where no factor is known. Once a factor is found, support for continued efforts to decompose the cofactor is much weaker.

[QUOTE]Some examples:
- M1061 to 62 bits has been TF'd well beyond recommended parms because someone thought/hoped/wished that maybe the factor is just one bit higher. But being the lowest composite not yet factored there is a lot of strong interest is being the one to factor it.[/QUOTE]

M1061 has also had multiple P-1s and far more ECM than is warranted, including several thousand curves with B1=1000000 during the past few months. That's too low a bound to find factors much above 35 digits, but other ECM has established that it is highly unlikely to have a factor below 60 digits. M1061 is probably beyond ECM.

[QUOTE=lorgix;238275]Also 13-PRP, 17-PRP and 31-PRP.[/QUOTE]

Attached are all the factored prime-exponent Mersenne numbers from Eddington's list, for which the cofactors are known to be PRP, but not proven prime. Anyone fancy working through it to establish that they are PRP to several bases? Proving the smaller ones prime?

With a bit more work, it should be possible to massage his data files to obtain a list of factored prime-exponent Mersennes whose cofactors are status unknown. It might be worth PRP testing some of these.

Have I just started a new subproject?

I think a PRP test (or many, in different bases) should be fairy easy on those numbers.

Why don't you post them on a new factoring thread with the pfgw command line switches?

Luigi

[QUOTE=Mr. P-1;238281]Attached are ... prime-exponent Mersenne numbers ...[/QUOTE]

Either 7135 is prime or I screwed up somehow.

[QUOTE=Mr. P-1;238283]Either 7135 is prime or I screwed up somehow.[/QUOTE]

There is indeed a lot of composites in the list. The smallest prime exponents have been completely factored.

I fixed the list.