P-1 factoring anyone?

[LaurV]

Originally Posted by James Heinrich

For those who are fascinated by P-1 factors found thanks to the Brent-Suyama extension, I now have a list of known ones here:
http://mersenne-aries.sili.net/brent-suyama.php

Note: there are certainly far more than the 84 currently listed, but they'll appear slowly over the next few days as I crawl my database and fill in the k factorizations (and thereby the minimum required B1/B2 to compare with the actual B1/B2 used).

That is a nice job!

OTOH, I would doubt that some 64-66 bits factors (with astronomical k's!!) in that list were found by P-1 at all. They were reported as big composites by some workers, tricking PrimeNet to believe they are P-1 (see Axon thread here around iirc), but they were (some new, some previously known) clearly TF factors.

OTOTOH , if you are still here around, please have a look to my comment in the kepler thread related to some gtx690 being a dual chip card.

[Dubslow]

Originally Posted by LaurV

That is a nice job!

OTOH, I would doubt that some 64-66 bits factors (with astronomical k's!!) in that list were found by P-1 at all. They were reported as big composites by some workers, tricking PrimeNet to believe they are P-1 (see Axon thread here around iirc), but they were (some new, some previously known) clearly TF factors.

OTOTOH , if you are still here around, please have a look to my comment in the kepler thread related to some gtx690 being a dual chip card.

Factors can only appear on the list if a results file/line was uploaded to his website saying it was P-1 and giving the specific bounds used. Otherwise he couldn't do the min/actual calculation he does (and otherwise he wouldn't know for sure it was P-1, as you pointed out).

[cheesehead]

Originally Posted by James Heinrich

For those who are fascinated by P-1 factors found thanks to the Brent-Suyama extension, I now have a list of known ones here:
http://mersenne-aries.sili.net/brent-suyama.php

Note: there are certainly far more than the 84 currently listed, but they'll appear slowly over the next few days as I crawl my database and fill in the k factorizations (and thereby the minimum required B1/B2 to compare with the actual B1/B2 used).

http://mersenne-aries.sili.net/expon...etails=7854383 is an interesting case.

Suggestion for extra work for you to do when bored: On http://mersenne-aries.sili.net/brent-suyama.php change the "Minimum Required" heading and columns to four columns: minimum required B1/B2 with Brent-Suyama, minimum required B1/B2 without Brent-Suyama.

Cases like 7854383 show why minimum required B1 could be different between with and without Brent-Suyama, unless I'm mistaken. Please enlighten me if I'm mistaken.

Even snazzier would be to show the extra columns only when there's a B1 difference, as with 7854383. But you may not be that bored for a long time, so ...

[LaurV]

Originally Posted by Dubslow

Factors can only appear on the list if a results file/line was uploaded to his website saying it was P-1 and giving the specific bounds used. Otherwise he couldn't do the min/actual calculation he does (and otherwise he wouldn't know for sure it was P-1, as you pointed out).

I didn't know that, sorry. I misinterpreted his affirmation about "crawling" as "crawling the PrimeNet database". There, factors found with P-1 appear as "F-PM1", and the others found by TF appears simple as "F". But reporting a big composite factor as P-1, results in marking both smaller factors as P-1. You can in fact TF one exponent, and if you are lucky to find 2 factors, then you report their product and get a big jump in P-1 credit.

[Dubslow]

Originally Posted by LaurV

I didn't know that, sorry. I misinterpreted his affirmation about "crawling" as "crawling the PrimeNet database". There, factors found with P-1 appear as "F-PM1", and the others found by TF appears simple as "F". But reporting a big composite factor as P-1, results in marking both smaller factors as P-1. You can in fact TF one exponent, and if you are lucky to find 2 factors, then you report their product and get a big jump in P-1 credit.

True, but PrimeNet doesn't record the method used in the public tables (like Factor Report) (much less the actual P-1 bounds); the type determination is only for credit purposes.

However, since very few users actually upload their results to Mersenne-aries, it might be worth it to James to crawl through the factors and look for those with factors more than a few bits above standard TF, and perhaps put those in a separate table marked "possible B-S factors".

Originally Posted by cheesehead

http://mersenne-aries.sili.net/expon...etails=7854383 is an interesting case.

Suggestion for extra work for you to do when bored: On http://mersenne-aries.sili.net/brent-suyama.php change the "Minimum Required" heading and columns to four columns: minimum required B1/B2 with Brent-Suyama, minimum required B1/B2 without Brent-Suyama.

Cases like 7854383 show why minimum required B1 could be different between with and without Brent-Suyama, unless I'm mistaken. Please enlighten me if I'm mistaken.

Even snazzier would be to show the extra columns only when there's a B1 difference, as with 7854383. But you may not be that bored for a long time, so ...

The problem is that Brent-Suyama depends heavily on what bounds are used and the "relative prime" count that Prime95 prints. It's more or less a random crap shoot above B2, as far as which particular FCs are tested, depending on B2 (and even then on the RP count like I just mentioned). See, for example M54699223 -- flash had seen a long dearth of S2 factors, and so tested his machine against this factor -- with a higher B2, he actually missed the B-S factor.
(Edit: That entire page of that second link, and the first post of the following page is about B-S and P-1. It's worth reading the page in its entirety -- among other discussions, there's a slightly more extended analogy.)

The point is there isn't a "minimum required with B-S" because it's a crap shoot. (If it weren't a crap shoot, that'd be the same as just testing to the higher B2.)

[LaurV]

Originally Posted by Dubslow

True, but PrimeNet doesn't record the method used in the public tables (like Factor Report)

That's why the "crawling" part: crawling through the "exponent status" pages and extracting exponents having "F-PM1" keyword :D. Of course, as I said, I completely forgot the fact that James keeps his own DB with history (contrary to PrimeNet where the history is gone when a factor is found).

[aketilander]

Originally Posted by LaurV

I completely forgot the fact that James keeps his own DB with history (contrary to PrimeNet where the history is gone when a factor is found).

I actually have a question about this. Is the history completely erased from the database or is it that it is not any longer displayed? You can for instance find LL-results for a specific exponent in the database even if a factor is found, but if you use report_exponent you only get information about the factor.

That is: How much of old results are still kept in the database? Is something at all erased? Is it possible to retrieve all information in database for a specific exponent if you would like to even in cases when a factor has been found later?

[Dubslow]

Originally Posted by aketilander

That is: How much of old results are still kept in the database? Is something at all erased? Is it possible to retrieve all information in database for a specific exponent if you would like to even in cases when a factor has been found later?

I suspect not, though of course I have no way to prove it. Database size is a major concern for PrimeNet -- and any factor found means space saved, with the current (assumed but not proven) policies in place.

[LaurV]

The history is not erased, just hidden and impossible to access anymore for commoners (like us). The proof is the fact that when you access your own LL** history, beside of "verified", "unverified" and "bad" results, there will be also a "Test results where factor was found later" section (I have a couple of them in my list). This means I did a LL, it was verified (or not), but later a factor was found. The DB remembers exactly the exponent's history (that is, who was the guy who did the initial LL, double check LL, maybe what type of factoring was used to find the factor, etc).

**in the link you have to replace yourUserId, with the real one, and must be logged on
edit: which is case sensitive :D found it in the hard way

[James Heinrich]

Originally Posted by Dubslow

However, since very few users actually upload their results to Mersenne-aries, it might be worth it to James to crawl through the factors and look for those with factors more than a few bits above standard TF, and perhaps put those in a separate table marked "possible B-S factors".

One day, possibly, eventually, I'll crawl through my list of known factors that have no known method of discovery and try and guess which was used. But that's not something I'm planning on doing anytime soon.

[James Heinrich]

Originally Posted by LaurV

OTOH, I would doubt that some 64-66 bits factors (with astronomical k's!!) in that list were found by P-1 at all.

Do you have a specific example I could look at?
As has been observed elsewhere, PrimeNet isn't very good at (a) knowing which manual results are TF vs P-1 (often assigning P-1 credit to TF results), and (b) reporting what bounds were used when a TF factor is found (which, of course, would also eliminate problem (a)).

Originally Posted by Dubslow

Factors can only appear on the list if a results file/line was uploaded to his website saying it was P-1 and giving the specific bounds used. Otherwise he couldn't do the min/actual calculation he does (and otherwise he wouldn't know for sure it was P-1, as you pointed out).

Quite right. I have many spidered-from-PrimeNet "PM1" factors in my database, but since PrimeNet doesn't tell what bounds were used when a PM1 factor was found that's not much use in this case. I can calculate what bounds would be required to find via normal P-1, but without knowing what bounds were used there's no way to know if Brent-Suyama was invoked.

Originally Posted by cheesehead

http://mersenne-aries.sili.net/M7854383 is an interesting case.

It is. It's the "very rare" case axn talked about when he outlined the algorithm for finding B1/B2:

If largest has a power > 1 (very rare), set B1=B2=large^power. Stop. (only stage 1 can find this one. stage 2 not needed)

Originally Posted by cheesehead

change the "Minimum Required" heading and columns to four columns: minimum required B1/B2 with Brent-Suyama, minimum required B1/B2 without Brent-Suyama.

The "Minimum Requied" B1/B2 is for regular P-1 with no Brent-Suyama extension, and is easily calculated. The minimum required bounds for Brent-Suyama to find the factor are nebulous at best, and don't actually translate into minimum bounds per se.
For example: M54,699,223 was found by Dubslow with B1=475,000/B2=8,906,250. But flashjh was unable to replicate the discovery with the slightly-higher bounds of B1=475,000/B2=9,025,000. It seems this is because a different number of relative primes was selected, and that affects how the Brent-Suyama extension works. So describing a "minimum B1/B2" is valid for regular P-1 (these or larger bounds will always find said factor), but not valid for Brent-Suyama extension.