Require P-1 and other factoring work to be done on reliable machines

[Madpoo]

Originally Posted by tha

To further clarify my intentions:

My most recent found exponent 10444177 has had some P-1 being done on it by some unknown machine. Given the B1 and B2 values that were used the machine should have found this factor, unless, and only unless, the machine was flaky.

As the factor found later proved, the machine was flaky.

That is indeed one example. I tried it myself just to confirm (leave nothing to chance, including the possibility that Prime95 is missing it consistently):
M10444177 has a factor: 62822149496547732721 (P-1, B1=120000, B2=2010000, E=6)

The user who missed it was using:
Linux,Prime95,v20

That same user went on to do an LL test on it which completed 2 months after the P-1 result was checked in (those are the first 2 "anonymous" results you'll see at M10444177 )

Too bad they missed the factor that first time...would have saved them 2 months of work back in 2000, plus the extra time for the double-check in 2003.

If it weren't for people doing TF to higher levels ("tha" in this case) we wouldn't have known.

[Madpoo]

Originally Posted by Madpoo

...
The user who missed it was using:
Linux,Prime95,v20
...

If anyone cares, I went through the other 20 times that users submitted a "P-1 no factor found" result and re-ran with the same B1/B2. No factors found... whatever happened, one time glitch I guess.

[tha]

Originally Posted by Madpoo

If anyone cares, I went through the other 20 times that users submitted a "P-1 no factor found" result and re-ran with the same B1/B2. No factors found... whatever happened, one time glitch I guess.

20 P-1 runs of a single machine is statistically pretty insignificant since the chance that an average P-1 returns a factor is about 1 in 20.

[tha]

Originally Posted by Madpoo

If someone wants to provide me with an easily digestible formula (as in it could be done in SQL) to take a found-factor and then see if prior P-1 "misses" with certain bounds should have found it, no doubts or ifs/ands/buts, then I'll try to query the data for cases like that.

These 35 exponents each had a P-1 run on them that failed to turn up a factor, while given their B1/B2 bounds should have. If we can figure out how many different machines were working on them that would provide us interesting data.

M12,961,177
M12,930,067
M12,911,999
M12,856,729
M12,815,641
M12,782,239
M12,766,759
M12,761,257
M12,755,521
M12,748,381
M12,709,261
M12,706,367
M12,661,399
M12,597,163
M12,586,247
M12,574,763
M12,560,221
M12,526,721
M12,503,419
M12,497,273
M12,474,029
M12,461,737
M12,448,201
M12,428,909
M12,404,627
M12,381,949
M12,379,229
M12,329,657
M12,258,083
M12,148,093
M12,127,879
M12,123,649
M12,111,313
M12,067,273
M12,027,481

[TheMawn]

Originally Posted by Madpoo

If someone wants to provide me with an easily digestible formula (as in it could be done in SQL) to take a found-factor and then see if prior P-1 "misses" with certain bounds should have found it, no doubts or ifs/ands/buts, then I'll try to query the data for cases like that.

You need something to quickly factor small-ish numbers.

All factors for Mersenne numbers are of the form 2kp+1. If you take the found factor, subtract 1, and factor that result, you will have at the very least, one power of two and one power of the exponent.

Ignoring the factor equal to the exponent, if the largest is less than B2, and the second-largest is less than B1, that is a P-1 miss.


So,

• Take the known factor, and subtract 1.
• Divide by the Exponent P and by 2, while you're at it.
• Divide the remainder into all its factors.
• Take note of the two largest factors including their power (if you have 2⁴ x 5 x 17, then the largest is 17 and the second-largest is 16), and compare those to B1 and B2 as mentioned above.

[Prime95]

Originally Posted by tha

These 35 exponents each had a P-1 run on them that failed to turn up a factor, while given their B1/B2 bounds should have. If we can figure out how many different machines were working on them that would provide us interesting data.

and how many versions of prime95. The earliest p95 versions could easily have had bugs.

[science_man_88]

Originally Posted by TheMawn

You need something to quickly factor small-ish numbers.

All factors for Mersenne numbers are of the form 2kp+1. If you take the found factor, subtract 1, and factor that result, you will have at the very least, one power of two and one power of the exponent.

Ignoring the factor equal to the exponent, if the largest is less than B2, and the second-largest is less than B1, that is a P-1 miss.


So,

• Take the known factor, and subtract 1.
• Divide by the Exponent P and by 2, while you're at it.
• Divide the remainder into all its factors.
• Take note of the two largest factors including their power (if you have 2⁴ x 5 x 17, then the largest is 17 and the second-largest is 16), and compare those to B1 and B2 as mentioned above.

just thought I'd add in:

Originally Posted by http://www.mersennewiki.org/index.php/Brent-Suyama_extension

The Brent-Suyama extension to the P-1 Factorization Method allows the possibility of finding factors outside the normal range expected from the P-1 bounds.

[Madpoo]

Originally Posted by TheMawn

You need something to quickly factor small-ish numbers.

All factors for Mersenne numbers are of the form 2kp+1. If you take the found factor, subtract 1, and factor that result, you will have at the very least, one power of two and one power of the exponent.

Ignoring the factor equal to the exponent, if the largest is less than B2, and the second-largest is less than B1, that is a P-1 miss.


So,

• Take the known factor, and subtract 1.
• Divide by the Exponent P and by 2, while you're at it.
• Divide the remainder into all its factors.
• Take note of the two largest factors including their power (if you have 2⁴ x 5 x 17, then the largest is 17 and the second-largest is 16), and compare those to B1 and B2 as mentioned above.

Well, it seems straightforward enough except I'd probably have to pre-factor things using YAFU or something in bulk and then create a table of resulting #'s to work from. I probably wouldn't get to that in a while.

James has a lot (all?) of the same factor data on mersenne.ca and might be interested in tackling that... no idea (I don't mean to volunteer him for something he doesn't care about )

I could at least look at that list tha provided and see if there's any commonalities.

[Madpoo]

Originally Posted by Madpoo

Well, it seems straightforward enough except I'd probably have to pre-factor things using YAFU or something in bulk and then create a table of resulting #'s to work from. I probably wouldn't get to that in a while.

James has a lot (all?) of the same factor data on mersenne.ca and might be interested in tackling that... no idea (I don't mean to volunteer him for something he doesn't care about )

I could at least look at that list tha provided and see if there's any commonalities.

There's a user "Spicer" that contributed 3 of those misses. I manually checked a small handful of the 40 other P-1 runs that user did where a factor was found later. Out of the maybe 5 or so I checked, I found at least one (if I'm doing it right):
M10853081

Specifically it seems like the factor should have been found with B1=130000, B2=2275000

To do any kind of systematic check I'd need some way to have YAFU (or whatever... I'm not particular) spit out those top two factors in some parse-able way. I don't want to have to script something to look at the text output of "yafu factor(xxx)" and figure out which ones to use... that's too much work for me.

Meanwhile on the database side I can break out the B1/B2 values of any P-1 attempts that came up empty, but a factor was found later by whatever method (TF, P-1, ECM, doesn't matter). The only thing needed to make it all do something interesting is the two factors to compare to the bounds and I'm not seeing any easy way to get that without putting more time into it than I care to do. LOL

FYI, that user was using "Windows,Prime95,v20,NT service" for a lot of those 43 where a factor was found later (and also some v21/v22 later on). Not all were P-1 misses, but in 4 of the cases it looks like a miss. That same user has checked in 2250 total "no factor by P-1" results and if they missed 4 so far, I guess it's possible more were missed. Of the 43 where a factor was found later, I know 4 were definite P-1 misses, another 4 I checked by hand were fine, and I don't know about the rest.

[TObject]

BTW, is there a rule now in place that a machine will not receive P1 work until it has a few double-checks completed?

Just launched a new machine with 30 GB of memory dedicated to Prime95, and all that memory sits unused, because the machine keeps getting double-check assignments despite the P1 Large work type selected.

[chalsall]

Originally Posted by TObject

BTW, is there a rule now in place that a machine will not receive P1 work until it has a few double-checks completed?

Don't know for sure, but possibly a side-effect of the new assignment rules.

Iff this theory is correct, your machine should start receiving P-1 assignments after two matching DCs are returned.