Anyone factoring <5M?

[cheesehead]

Originally Posted by markr

Here's a thread from a long, long time back:
http://www.mersenneforum.org/showthread.php?t=1425

Thanks!

Two notes from re-examining that thread after all these years:

- -

1. In post #9 dswanson correctly points out that "ribwoods" (that's me, before I was "cheesehead" here) misinterpreted the second column, but he himself misinterprets me when he speculated that I had

"missed the point, which is that nofactor.txt had claimed that this exponent had no factor below 2^62. So it is indeed a trial-factoring failure."

No, I had not missed that point. And, I now think, we were both partly right about whether the misses were a failure of "trial factoring" -- depending on whether one considers "trial factoring" to mean only the actual trial-factoring search computations on potential factors, or to mean not only the search computations but also the setup and reporting of such searches.

- -

2. According to all the evidence I've seen, both back then and now, the most likely cause of those missed factors was that (note the part B revision from what I stated above in post #9):

Some entire power-of-2 ranges of TF results on a few exponents were not properly reported, because either:

A) mistakes in setting up the TF runs accidentally omitted specifying some power-of-2 ranges, or

B) a few TF runs on some power-of-2 ranges were executed but never reported, but the database was erroneously updated to show that those power-of-2 ranges had been searched and reported unsuccessful. (In some cases, the missing reports would have shown a factor found, and those factors are what we're rediscovering since then.)

Possibilities A and B were both explored in a 9 Oct 2001 mailing list posting by Reto Keiser, quoted in "Missed small factors" thread post #17:

While completing some trial factoring in the 60 million range I noticed, that the prime95 checksum of factoring from 65 to 66 bits and from 66 to 68 bits are the same (I did this two parts of the same exponent on different computers). That means that it is easily possible that some mistakes can happen, when someone writes the 'Factor=' line into the worktodo file.

-- possibility (A)

Another reason might be, that one person ran a broadband factoring range from 55 to 58 bits on one computer, from 58 to 59 on another (to split up the work) and forgot to check in the former results. As there is no information about the starting bit in the result file, the primenet server is not able to detect that problem.

-- possibility (B)

There also could be other reasons than forgetfulness for failure to check in results on some power-of-2 ranges.

- -

Personally, I think the evidence we have does not support the theory that the computations examining whether potential factors were actual factors were at fault in some TF software, but is all consistent with the theory that the missed factors were due to a setup or reporting failure.

[Prime95]

Any missed factors for exponents below 2,000,000 could easily be due to a program bug. There were several such bugs in the earliest prime95 versions. These exponents were likely trial factored in the 1996 - 1999 time frame.

[garo]

Hmm! For some reason, when I first tried to reserve these exponents for TF from 61->62, I got an error saying no more TF is needed and the exponents were removed from my wtd. But now it seems I am able to get the exponents reserved without any trouble. I'm doing a P-1 on some exponents as well. generally, those with B1,B2 at 20k,20k or less.

[garo]

Originally Posted by markr

I'm doing TF from 61 to 62, currently in the 48xxxxx range. Using the LMH method to have them assigned in PrimeNet, I simply take the highest currently unassigned, queuing up a few days work at a time.

Ahead of that effort I do P-1 to fairly high bounds on the few exponents that haven't had "enough" P-1. This actually finds more factors than the TF effort, measured by success rate.

I took some exponents at 4.7M. I have reserved them via PrimeNet. What is your definition of "enough" P-1?

[markr]

Originally Posted by garo

I took some exponents at 4.7M. I have reserved them via PrimeNet. What is your definition of "enough" P-1?

Glad you got it working through PrimeNet, garo. If we're all using PrimeNet we can work in the same ranges & we won't wind up wasting work. There are lots of ECM assignments in the 4M range, too.

Quite arbitrarily, anything with B2 < 200000, I do to 100000,2500000. IIRC, roughly 5% find a factor (although my bounds were slightly lower then). TF by one bit-level finds ~1.5%.

Having them assigned in PrimeNet is not so simple, though. To specify the bounds, one needs "Pminus1" lines in the worktodo, but PrimeNet won't accept them. (It says "unsupported assignment work type: 3".) So I put in "Pfactor" lines, PrimeNet registers them & supplies the AIDs, and then I change them to what I want, leaving the AIDs in.

[S485122]

Originally Posted by markr

Having them assigned in PrimeNet is not so simple, though. To specify the bounds, one needs "Pminus1" lines in the worktodo, but PrimeNet won't accept them. (It says "unsupported assignment work type: 3".) So I put in "Pfactor" lines, PrimeNet registers them & supplies the AIDs, and then I change them to what I want, leaving the AIDs in.

Since Pfactor lines are accepted you can change the last parameter of Pfactor lines to increase the bounds :

Woktodo.txt line B1 bound  B2 bound
Pfactor=1,2,4700021,-1,61,1   25000   343750
Pfactor=1,2,4700021,-1,61,2   60000   960000
Pfactor=1,2,4700021,-1,61,3   95000  1781250
Pfactor=1,2,4700021,-1,61,4  130000  2697500
Pfactor=1,2,4700021,-1,61,5  165000  3671250
...

Of course the bounds are not so beautifully rounded numbers then :-)

Jacob

[markr]

Originally Posted by S485122

Of course the bounds are not so beautifully rounded numbers then :-)

No, but it is a much simpler procedure! Thank you, Jacob.

[garo]

You can use non-integers for bounds as well. Try 3.2. I used the standard "2" tests saved and I got bounds of 60/65k and 1200/1218k with 1.5GB of memory (just a test run on my main rig) and a 4.42% chance of finding a factor. I'll be lazy with the P-1 and only do it on exponents with B2 < 100k. I generally have rotten luck finding factors with P-1 - though I have been on a roll lately and found 5 factors in the 51-53M range in the past month.

PS: I just realized that even though you get a 5% chance of finding a factor - the P-1 that is already done also has a chance of finding a factor - usually about 2.5% according to the typical bound - so the effectiveness of your P-1 is halved.

[markr]

Originally Posted by garo

You can use non-integers for bounds as well. Try 3.2. I used the standard "2" tests saved and I got bounds of 60/65k and 1200/1218k with 1.5GB of memory (just a test run on my main rig) and a 4.42% chance of finding a factor.

Thanks for the tip about non-integers, garo.

I generally have rotten luck finding factors with P-1 - though I have been on a roll lately and found 5 factors in the 51-53M range in the past month.

Five factors in P-1-large is excellent! My last batch of 25 P-1 in M48xxxxx had four factors, so anything's possible... ... it makes up for the batches with 0 or 1 found. Happy hunting!

PS: I just realized that even though you get a 5% chance of finding a factor - the P-1 that is already done also has a chance of finding a factor - usually about 2.5% according to the typical bound - so the effectiveness of your P-1 is halved.

That some P-1 was already done is one reason why I opted for highish bounds.

[garo]

And another 53M factor last night!

You do have a better chance of finding a factor with highish bounds but I'd say do an efficiency analysis vs. TF to 62 to TF to 63. With higher bounds you are spending more time with a smaller additional chance of finding a factor so doing TF for 1 bit first might be better.

BTW, I'm not doing any more TF in this range after my current assignments finish. I'm setting that machine back to TF-LMH as I have decided against any babysitting.

[cheesehead]

Originally Posted by Prime95

Any missed factors for exponents below 2,000,000 could easily be due to a program bug. There were several such bugs in the earliest prime95 versions. These exponents were likely trial factored in the 1996 - 1999 time frame.

My recollection (already shown to be fallible :) is that after those bug fixes, someone went back through all reports from the buggy version and re-ran all unsuccessful TFs that had been done with the buggy version.

Another incorrect recollection? (* sigh *) Or was that done only after some bug fixes but not others?