Help me understand P-1 factoring

[Keroberts1]

I've been doing alot of thinking about how best to choose B1 and B2s and I don't think the software is doing it in the most efficient manner. I was hopping someone who knows a good deal about the software and how it chooses the most appropriate bounds could speak with me through IM and perhaps answer a few of my questions. Perhaps i might have a few ideas about how to make it more efficient. I'm not an expert with computers by any means and i have next to no programming experience. I'm also not an expert in number theory but i am a fast learner. I do have a little bit of experience with statistics and this i believe is the best way to work out this problem. By this i mean i am taking a statistics course and have been trying to apply it to what I'm seeing here and some things don't add up. All i need to know is how the bounds are chosen now to decide if there are any ways in which i could help. I will probably have more questions after each answer so i thought this could go alot faster through a direct communication with an expert in the program. If this can be done please someone send me a message with an AIM name and i will watch for you to be online and ofcourse I promise not to be a pest and any time you're available to speak with me is fine. If no one wants to speak directly but could offer some insight into my questions so far I'd love to see some replys.

Thankyou very much

Kroberts5

[Keroberts1]

Also if anyone who has completed a P-1 range greater than say 20,000 or more and coule tell me what K,N-values yeilded factors and what those factors were plus waht bounds were used ot find them I would appreciate that also.

If anyone is willing to help me on these issues i can't promise i will produce any results or help them back in any way but i would like to know more about how things work and see if i can help. Basically anyone who's willing to humor me will really make my day. I'd really appreciate how active this fourum is and how often many of the regulars are willing to answers each others questions and often even entertain pleasant conversations and debates. It really seems like a true online community. SO... I'm basically just looking for some realtime community communications. Could some chatrooms be setup for this fourum? Are they existing now? Perhaps we can setup some meeting times say once a month where people can throw out ideas and get immediate answers to questions.

[hhh]

I don't want to break your pace, but I just remember when I asked Prime95 (George Woltman) what is the formula by whitch the bounds are chosen and when he answered that it is too horribly difficult to post.
I guess though there could be made some improvement, especially in the case where Stage1 and 2 are done on different computers with different memory, and I consider it an interesting problem. But I wonder if we find somebody to explain us the details needed.
Though, I think it is a feasable statistics problem. We could look up all the factors found yet, their necessary bounds, times to complete on different computer platforms with different memory, optimize it numerically, but hey that's a bunch of work and it would be a pity to reinvent the wheel.
So if you get some information, I'm on board, but I wouldn't be disappointed if this thread ends up remaining good intentions.
H.

[Keroberts1]

i do believe it will probably end up just being good intentions but there isn't muc helse to do at 4:46 in the morning and i am just waiting for it to be early enoug hto go to work. Here is my thoughts so far....

There are 2 different kinds of factors we find...

small factors found in sieving
smooth factors found in P-1

remember P-1 just looks fo how smooth a factor is and it is searching a wide range of digit lengths.

The smaller factors (under 2 or 3 thousand T) can be so incredibly unsmooth that P-1 could never find them... and usually are.

now here's the task at hand.

what is the normal distribution of factor lengths in at a N value of different sizes.

Of these factors what is the normal distribution of factor smoothness.

When there are no factors below a certain digit size (sieve boundary) how does this alter the expected factor distribution of each.

What is the average ratio between second largest and largest factor components (for calculating best B1 B2 values).

What is the anmount of time for a GCD for most tests of various sizes and whether it would be best to perform them in the middle of tests to save time incase a factor is already available.

(remember as tests get larger is is likely that there will be more small factors and smooth factors!) factoring saves more work. Therefore factoring will be removing more cadidates than it currently is perhaps as many as 5%.

What is speed differance between PRP, Sieve, Stage1 P-1, stage 2 P-1.

hardware differances also.

I'd like to see a complete factorization of a large number to see how factor distribution works out in real world. I believe there is a project currently working on a complete factorization of a proth number. Does anyone know what its current status is?

I'll probably have more to add later but I haven't got all the time in the owrld right now o I'll speak more later if anyone expresses interest in my ramblings.

[Greenbank]

Does this help:- http://www.greenbank.org/sob/p-1.html

http://www.greenbank.org/sob/p-1_limit.html is for 9M <= n <= 11M

The tables show the percentages (in brackets) of factors found that would have been found with those B1 and B2 values.

Haven't updated it for a while but it should be a good place to start.

[garo]

Read this:

http://www.sslug.dk/~grove/sbfactor/...ng_bounds.html

[Keroberts1]

greenbank i believe that is extremely useful it would help some if it was done for a complete factorization of a single number so i could also see what the factor distribution iswithin a single n=10-11mil test. of course this is not likely to happen so we'll take what we get. The stats are a little biased being that many of the factors were found using P-1 and many were found using sieve. This changes alot since these are completely different varieties of factors.

[Nuri]

focus on 51 bit and plus for P-1 effectiveness idea...

yes, there are some 51 bit plus factors through sieve, but really rare

yes, there are some 50 bit and less factors found through P-1, but again very rare compared to the total factors found there

[hhh]

Greenbank you are an ace, and probably one of the most valuable members to this little, charmful community.

Though there are things I don't understand about the data: in the 9M-11M sheet, the sums are

46bit 4958 factors
47bit 3729 factors
48bit 3352 factors
49bit 9808 factors
50bit 8286 factors


What is this coincidence with the moment when we swiched to the larger dat-dile, though it should be only factors for 9M-11M?

What would be most useful would be the same data for the last digit level we sieved (now it would be 48.x-49.x), for the last range of N values completely factored (know it would be about 9.5M-10.5M). Having these data, one could optimize the bounds for this set (already done) and take these bounds for the next set to factor.

I know that I will have even better ideas involving quantiles, but I have to concentrate, tomorrow morning, impossible right now.

As for the idea with the complete factorization, I don't see the point as we are trying to find one factor, and one of the smallest. It would be an example without any statistical worth.

See you, H.

[Greenbank]

We can't even find a single factor for 24737*2^991+1, what hope is there of completely factoring something up in the range of n=10M?

Anyway, I've got to move everything that creates those tables (a mysql db and a load of perl) over to my new Mac, then I'll run it against the latest results.txt file.

I'll also generate more tables (with tighter bounds).

Will be a couple of weeks at least as I'm busy at work and there's that small matter of Christmas.

[Nuri]

Greenbank, are you running the script for unique factors only, or does it include excluded and duplicates as well?

[vjs]

Elevensmooth is doing what keroberts suggested. (Sort of anyways)

Their exponent is a n~3M and it doesn't look like it will completely factor anytime soon.

A 10M is next to impossible with current technology, plus any information gained is probably no better than stat predicitions anyways.

Keroberts, check out elevensmooth's FAQ I think you'll find what your looking for.

[hhh]

Please consider the wikipedia article I created.

http://wiki.seventeenorbust.com/inde...d_optimisation

Perhaps we can move there and better keep track of the achievements.

H.

[Greenbank]

Originally posted by Nuri
Greenbank, are you running the script for unique factors only, or does it include excluded and duplicates as well?

That data was based on a mixture of unique duplicate and excluded.

Ideally I want to have two seperate versions of the tables. One for unique factors only (i.e. results.txt) and the other for all factors (unique/duplicate/excluded).

[Nuri]

Thanks for the answer.

[Anitaheiff]

Morning all,
I have recently got my Grandfather's attestation document I think, but I don't understand any of what it says other than his Army number. Can someone please take a look and help me understand what all the numbers, dates and other narratives man. For instance what does S/C mean then why is it crossed out. Also what does 're posted to L/AA' mean and 'z'T?
Many thanks