Anyone factoring <5M?

[garo]

I think most of the range has had at least 3 curves at 25 digits(2^83) done. That has a good chance of capturing factors under 66 bits - by my totally wild-ass calculation about a 1 in 3 chance. That sort of tallies with your experience - you just need to extrapolate my wild-ass calculation for 63 bits.

Edit: An interested reader could go and read the Silverman Wagstaff paper and calculate a more precise answer. I learnt how to do it about 5 years ago but don't have time to relearn it now.

[chalsall]

Originally Posted by markr

Anyone else working in this area, or thinking about it?

I occasionally have a few of my machines working in the <1M range, bring the exponents from 60 to 61.

Rather silly really, I know. Out of 3964 tested, only 5 factors found (0.1261%)....

[petrw1]

Originally Posted by markr

Someone cleaned up the few remaining above 4.5M regardless that they were assigned to others for ecm, or to me.

An "Exponent Status" report well tell you who in case it is someone on this forum that you can contact.

[cheesehead]

Originally Posted by alpertron

When running a TF and a hardware problem occurs, the missing factor will never be found.

Never say never.

a) What accounts for the multiple cases in which earlier-TF-missed factors actually were found?

b) What exempts ECM from hardware problems? :)

[markr]

Originally Posted by garo

@markr, petrw1
Have you found any factors guys or have the ECM folks taken them all?

There's still enough. A quick bit of counting text strings in current & old results files gives 113 factored out of 10181 attempts, for TF from 61 to 62 'bits' between about 4500000 & 5000000. That's 1.1%.

I'm only doing this TF because of two machines I have that are still in use, old Athlon XP's which are good below 2^64 and really shine below 2^62. Doing more P-1 on exponents in this region with relatively little already done is far more productive, even though a P-1 result with the parameters I use is less effort than TF, as measured by the credit.

[markr]

Originally Posted by petrw1

An "Exponent Status" report well tell you who in case it is someone on this forum that you can contact.

I did check who it was. I'm hoping it was a one-off.

[alpertron]

Originally Posted by cheesehead

Never say never.

a) What accounts for the multiple cases in which earlier-TF-missed factors actually were found?

b) What exempts ECM from hardware problems? :)

a) These cases were software errors, not hardware errors, as recognized by Woltman, and the factors were found by rerunning all bit levels. Some of the missing factors were found by ECM.

b) In that case the missing factors will be found in another computer using more curves. This will need to be done anyway when no factors are found.

Also notice that after some bit level threshold which depend on the exponent, you will find more results per unit of time using ECM than using TF. For smaller exponents, that bit level is lower, so it is recommended not to use TF but ECM instead.

[lorgix]

Originally Posted by garo

I am planning to do some exponents from 61 to 62 or 63. They cannot be assigned via PrimeNet so I just wanted to check here first.

I've taken a special interest in doing fast P-1 in the area of ~4.42-4.54M.

The TF limits on the ones I'm currently looking at are about 50:50::61:62

(I also did 61-62 on five 4.482<exponents<4.485M. -> ~0.343GHz-Days & 0 factors found.)

I'll probably keep working my way down. Now doing P-1 with FFT length 224-256K.

I'm also taking a closer look at 1~1.4M.


Anyway, the chunks you're referring to should be so fast that interference is unlikely, no?

[markr]

Originally Posted by lorgix

I've taken a special interest in doing fast P-1 in the area of ~4.42-4.54M.

The TF limits on the ones I'm currently looking at are about 50:50::61:62

(I also did 61-62 on five 4.482<exponents<4.485M. -> ~0.343GHz-Days & 0 factors found.)

I'll probably keep working my way down. Now doing P-1 with FFT length 224-256K.

I'm also taking a closer look at 1~1.4M.


Anyway, the chunks you're referring to should be so fast that interference is unlikely, no?

Welcome to the neighborhood!

My two TF machines are currently factoring to 2^62 in the 4.48M-4.50M area, with >100 exponents assigned to them. I'm working my way down, giving them bunches of exponents much as described in this thread, avoiding others' assignments. Pragmatically, you're correct - there's not much chance of duplicated effort. But it's not difficult to avoid already-assigned exponents.

Just out of interest, do you use pfactor or pminus1 lines in your worktodo for your P-1 work, and what kind of bounds?

Pfactor=k,b,n,c,how_far_factored,num_primality_tests_saved
Pminus1=k,b,n,c,B1,B2

[lorgix]

Originally Posted by markr

Welcome to the neighborhood!

My two TF machines are currently factoring to 2^62 in the 4.48M-4.50M area, with >100 exponents assigned to them. I'm working my way down, giving them bunches of exponents much as described in this thread, avoiding others' assignments. Pragmatically, you're correct - there's not much chance of duplicated effort. But it's not difficult to avoid already-assigned exponents.

Just out of interest, do you use pfactor or pminus1 lines in your worktodo for your P-1 work, and what kind of bounds?

Pfactor=k,b,n,c,how_far_factored,num_primality_tests_saved
Pminus1=k,b,n,c,B1,B2

Mostly I just looked for exponents that hadn't been factored very far. There was a wide range of different bounds. I decided to focus on exponents that had P-1 B2 less than 362500 (pretty arbitrary), and go through them methodically. I gave those that had only gone through TF to 61 a little preference. I used Pfactor, 3 tests saved. That ended up B1~80-100k B2~1.5-2M (stage 2 using 885MB). The "worst" cases before were B1:20k B2:200k.
I stayed away from exponents that were already assigned. I did happen to notice that I had done P-1 on exponents like the day after you had done TF on them.

Anyway, the yield was decent. Still, I have changed my strategy a bit.
Now being more of a part of the collaborative effort.

I now run two workers, one for each logical CPU. One is set to do server assigned TF when the WR-size LL-tests I've gathered are done (calcs that don't need a lot of memory), the other one is finishing off a few P-1 in the above mentioned interval (should be no more than 1.5days, I arbitrarily unregistered a few), and is then set to do ECM on small Mersennes (requires a lot of memory). So my plan is now to stick with server assigned TF and ECM and not do manually assigned exponents for a while. Although P-1 is sort of my "favorite", so I might throw in a few appropriately sized (>45M) exponents for that along with the ECMs (which are currently 5M+ btw). Gonna try to stick with this for a while.

Nice to know that there are more people out there interested in finding factors, not only for the purpose of excluding prime candidates.

Next time I go into a one person sub project I think I'm gonna put in a little more planning. I mean I'm probably more stubborn and relentless than my CPU... but that's not necessarily efficient. ;P

[markr]

Originally Posted by lorgix

Mostly I just looked for exponents that hadn't been factored very far. There was a wide range of different bounds. I decided to focus on exponents that had P-1 B2 less than 362500 (pretty arbitrary), and go through them methodically. I gave those that had only gone through TF to 61 a little preference. I used Pfactor, 3 tests saved. That ended up B1~80-100k B2~1.5-2M (stage 2 using 885MB). The "worst" cases before were B1:20k B2:200k.

The reason the "worst" cases you saw had B2=200000 is that I selected exponents with B2<200000 (arbitrarily) when I went through doing P-1 ahead of TF. I used Pfactor, set up so B1 & B2 were at least about 100000 & 2000000. In the 3M range I changed to selecting with B2<180000 because there's a lot of them, and bumped up the target bounds a bit. I'm below 3060000 now.

Lucky for me I went through your area of interest before you - I found my largest low-exponent factor there!

Good luck with the ECM work!