You have a point ... I can register a load as assignments but then my worktodo will have 1460 lines ... updating will torment the server.

[QUOTE=PageFault;299094]You have a point ... I can register a load as assignments but then my worktodo will have 1460 lines ... updating will torment the server.[/QUOTE]
I just set the days to report to 7, so it only hits once a week

[QUOTE=bcp19;299095]I just set the days to report to 7, so it only hits once a week[/QUOTE]If you're only doing these kinds of assignments, you could set to update only once a month; all the work should be done and reported complete before any updates are needed.

Sounds like a plan to me - I'll set the update to 30 days. I can knock off the whole batch in 50 days, about the time it takes for a first time test on the second core.

I am doing stage 2 in 30 minutes, 480 of 480 relative primes in one pass using 1735 MB of 1920 MB ram allocated. The BS extension is being used, results.txt shows E=6. The bounds are B1=95000 and B2=1662500 with the probability of finding a factor estimated at 3.9 %.

I hope I get lucky ... my entire history of P-1 success rate is 3.78 % ... I did better at TF, 4.9 % ...

[QUOTE=James Heinrich;299097]If you're only doing these kinds of assignments, you could set to update only once a month; all the work should be done and reported complete before any updates are needed.[/QUOTE]
With the program running, I could not select above 7, which is ok since I only have 1 core on the 8M and the rest LL.

[QUOTE=PageFault;299101]Sounds like a plan to me - I'll set the update to 30 days. I can knock off the whole batch in 50 days, about the time it takes for a first time test on the second core.

I am doing stage 2 in 30 minutes, 480 of 480 relative primes in one pass using 1735 MB of 1920 MB ram allocated. The BS extension is being used, results.txt shows E=6. The bounds are B1=95000 and B2=1662500 with the probability of finding a factor estimated at 3.9 %.

I hope I get lucky ... my entire history of P-1 success rate is 3.78 % ... I did better at TF, 4.9 % ...[/QUOTE]
Don't forget, those were P-1'd already, just poorly, so you may not find as many.

[QUOTE=bcp19;299103]With the program running, I could not select above 7, which is ok since I only have 1 core on the 8M and the rest LL.
[/QUOTE]

If you modify the text file yourself, you can choose almost anything you want, down to and including 0.04; for the first 6 months or so of my GIMPSing, my computer reported slightly more than once per hour :smile: (Of course, you'd be looking at 30 days, not once an hour :razz:)

Well, the easy factors have already been found and these tests didn't have the easy ones. We shall see the stat for the batch in about two months. The bounds are deeper than the original runs, significantly so.

Crap ... when I started this project I was doing similar ranges ... in the ancient ages ... I had a Pentium II, can't recall the total ram in the box but IIRC I allocated a massive 64 MB to prime95 ... too bad the results.txt files are long lost ...

In the ancient ages, we used to ask George for blocks of work and then set checkin at 59 days, making sure to do a manual communicate around 55 days. It was all good ...

[QUOTE=Dubslow;299104]If you modify the text file yourself, you can choose almost anything you want, down to and including 0.04; for the first 6 months or so of my GIMPSing, my computer reported slightly more than once per hour :smile: (Of course, you'd be looking at 30 days, not once an hour :razz:)[/QUOTE]

[QUOTE=PageFault;299106]In the ancient ages, we used to ask George for blocks of work and then set checkin at 59 days, making sure to do a manual communicate around 55 days. It was all good ...[/QUOTE]

Heh, I've only been at it a few weeks longer than my join date :razz: (then again, I was three when the project started :razz:)

[QUOTE=Dubslow;299107](then again, I was three when the project started :razz:)[/QUOTE]

Man... Kids these days... They just don't appreciate what is was like...

Walking five miles to the punched card reader...

Through blowing snow. Forty below...

Uphill in both directions.... :razz:

And we are all glad you're doing it. You'll be seasoned after a decade or so ... I first heard about GIMPS in my first year of engineering school. There was a faculty wide mandatory computer course, writing crude code in Fortan77. One of the assignments was a program to determine primality ... I think mine crapped out at tests around the number 64000 ...

[QUOTE=chalsall;299108]Man... Kids these days... They just don't appreciate what is was like...

Walking five miles to the punched card reader...

Through blowing snow. Forty below...

Uphill in both directions.... :razz:[/QUOTE]
My mom can tell me all about punched card readers... but the snow's all your fault for living in Canada :razz: (I do get my fair share of it in Illinois, though the -40 admittedly is something I haven't experienced.)

[QUOTE=PageFault;299109]And we are all glad you're doing it. You'll be seasoned after a decade or so ... I first heard about GIMPS in my first year of engineering school. There was a faculty wide mandatory computer course, writing crude code in Fortan77. One of the assignments was a program to determine primality ... I think mine crapped out at tests around the number 64000 ...[/QUOTE]
Heh, any quick 5 liner in any (reasonable) language you want can easily hit 10 digit+ numbers these days :razz:

I hear you ... in some parts of the world things are still hard though ... I recently returned from Africa. I spent 7 years there, until a coup d'etat chased me away. In the bush, the best means of data transfer was to strap the punch cards to the belly of a pet sheep ...

Seriously, I was travelling 100 km to the nearest internet cafe, with a connection equivalent to a 1990's dialup connection. It sucked ...

Anyone remember the early modems, where you put the telephone onto the little mike / speakers thing ... it looked like headphones ...

[QUOTE=chalsall;299108]Man... Kids these days... They just don't appreciate what is was like...

Walking five miles to the punched card reader...

Through blowing snow. Forty below...

Uphill in both directions.... :razz:[/QUOTE]

[QUOTE=PageFault;299113]Anyone remember the early modems, where you put the telephone onto the little mike / speakers thing ... it looked like headphones ...[/QUOTE]

Yes; in about 1978 I had a portable terminal from work to take home (was it a TI - Texas Instruments?) You put the phone handset in the rubber cups. It was a 300 baud modem and used a roll of thermal paper. It was like a little typewriter in a portable case.

[QUOTE=Dubslow;299111]My mom can tell me all about punched card readers... but the snow's all your fault for living in Canada :razz: (I do get my fair share of it in Illinois, though the -40 admittedly is something I haven't experienced.)


Heh, any quick 5 liner in any (reasonable) language you want can easily hit 10 digit+ numbers these days :razz:[/QUOTE]

When I was at the University of Illinois in 1976 we all thought that the self-service card reader was the greatest thing going. It sat on the counter and was convenient for inputting small student jobs. Learning PL/C as part of my MS in Library Science.

The University of Illinois is still one of the greatest research libraries in the world. It is the 3rd largest academic library system in the United States. Harvard, Yale, U of I.

Good God we are over that. Some of the young'uns have never seen a telephone like that ...

[QUOTE=Chuck;299118]When I was at the University of Illinois in 1976 we all thought that the self-service card reader was the greatest thing going. It sat on the counter and was convenient for inputting small student jobs. Learning PL/C as part of my MS in Library Science.

The University of Illinois is still one of the greatest research libraries in the world. It is the 3rd largest academic library system in the United States. Harvard, Yale, U of I.[/QUOTE]

I'm at UofI, and I just took my CS final last Friday :smile:
(You'll notice my location <-- is the bounds for a corridor stretching from Chambana to Chicagoland, so that I'm generally in the box at any given part of the year.)

[QUOTE=Chuck;299115] in about 1978 ... You put the phone handset in the rubber cups. It was a 300 baud modem[/QUOTE]
[URL="http://www.syssrc.com/html/museum/modem_noakes300.shtml"]Like this[/URL], or its father? :smile: Check also the links on the lower right side of the page.

(didn't find the link to the father but I know what you are saying)

[QUOTE=chalsall;299108]Man... Kids these days... They just don't appreciate what is was like...

Walking five miles to the punched card reader...

Through blowing snow. Forty below...

Uphill in both directions.... :razz:[/QUOTE]
Writing Z80 machine code via decimal numbers....

[QUOTE=LaurV;299129][URL="http://www.syssrc.com/html/museum/modem_noakes300.shtml"]Like this[/URL], or its father? :smile: Check also the links on the lower right side of the page.

(didn't find the link to the father but I know what you are saying)[/QUOTE]

No it was this one
[URL]http://www.computerhistory.org/collections/accession/X1612.99[/URL]

I remembered the name, the TI Silent 700. It had the modem built in behind the paper roll.

[QUOTE=Chuck;299115]Yes; in about 1978 I had a portable terminal from work to take home (was it a TI - Texas Instruments?) You put the phone handset in the rubber cups. It was a 300 baud modem and used a roll of thermal paper. It was like a little typewriter in a portable case.[/QUOTE]

We had a telephone connection like that at my high school, but it was only 75 baud IIRC. I know I can remember getting my first 1200 baud modem and being amazed at the speed. Course, since my early computers were a Timex-Sinclair 1000 with the 16K ram pack, an Atari 800 modified to 64K ram and the schools TRS-80, 1200 baud was more than enough.

[QUOTE=bcp19;299175]We had a telephone connection like that at my high school, but it was only 75 baud IIRC. I know I can remember getting my first 1200 baud modem and being amazed at the speed. Course, since my early computers were a Timex-Sinclair 1000 with the 16K ram pack, an Atari 800 modified to 64K ram and the schools TRS-80, 1200 baud was more than enough.[/QUOTE]

LOL... You know you're old when you nostalgically remember the thrill of upgrading from 110 baud... :smile:

When I first moved here to Barbados I had to pay something like $2000 USD a month for a (unreliable) 256 kb/s circuit. My house back in Canada at the time was dual homed, with a 1.5 mb/s ADSL connection and a 2 mb/s cable modem connection. Total cost of about $100 CAD a month.... :cry:

Hey kids!

By the time you are old geezers like us, there will have been many technological advances about which you'll love to reminisce for the then-kids, but human nature will (probably) be about the same. Study human nature -- that knowledge won't become as outdated as some other knowledge will.

[QUOTE=cheesehead;299180]Study human nature -- that knowledge won't become as outdated as some other knowledge will.[/QUOTE]

Wise words.

Perhaps that is why "The Prince" is still required reading....

Heh -- I was thinking "won't become outdated"... unless "we kids" advance technology to the point where we become merged with the machine anyways. :smile:

[QUOTE=Dubslow;299191]... unless "we kids" advance technology to the point where we become merged with the machine anyways. :smile:[/QUOTE]

Aren't you already?

[QUOTE=Dubslow;299191]Heh -- I was thinking "won't become outdated"... unless "we kids" advance technology to the point where we become merged with the machine anyways. :smile:[/QUOTE]Even more reason to study human nature now, so you'll know what you're messing with (or someone else is messing with).

[QUOTE=cheesehead;299213]Even more reason to study human nature now, so you'll know what you're messing with (or someone else is messing with).[/QUOTE]

Touché. :smile:

46 retests done on my range M83xxxxx: 1 factor found, Stage 1 (B1=95000).

I am surprised. I expected to find one or two in Stage 2 given that the first runs were very badly done and back then most people could not allocate close to 2 GB of ram (back then a hot rod would have been a P3 Katmai perhaps with 256 MB total ram). Stage 1 should have found this, or what gives?

1410 tests pending ...

[QUOTE=PageFault;299404]46 retests done on my range M83xxxxx: 1 factor found, Stage 1 (B1=95000). I am surprised. I expected to find one or two in Stage 2 given that the first runs were very badly done and back then most people could not allocate close to 2 GB of ram (back then a hot rod would have been a P3 Katmai perhaps with 256 MB total ram). Stage 1 should have found this, or what gives?[/QUOTE]Which exponent / factor? If you've submitted your results to [url]http://mersenne-aries.sili.net[/url] then you'll see where the factor falls on the P-1 graph and how it was missed by the first P-1 (whether B1 and/or B2 was too small to find it).

The "poorly done" P-1s may or may not have had stage 2 done, but either way the factor probability for that batch is somewhere just over 2%. Assuming you're giving sufficient RAM to achieve a nominal 5% probability, you'd expect around 3% to have factors (since 2% have already been found by the first round of P-1) -- 46 * 0.03 = 1.38, which is pretty close to the 1 you've found already.

The ~3% success rate isn't exciting, except by virtue of these exponents being small and being able to chew through a hundred or so of them per day (depending on what you're running it on, naturally).

[QUOTE=James Heinrich;299411]The ~3% success rate isn't exciting, except by virtue of these exponents being small and being able to chew through a hundred or so of them per day[/QUOTE]As a slightly larger sample size shows: my last batch of 697 exponents had 20 factors (2.87%).

James,

It isn't the incidence of factors, rather it is the finding of a factor in Stage 1. This should have been harvested as low hanging fruit the first time it was factored.

Perhaps the client should do more in Stage 1 if there is insufficient ram for a good Stage 2?

What I observed was a factor with B1=95000; the data on your page indicated B1=65000 for the first run.

I'll continue doing my range and I may try a hundred or so using the Pminus1 argument. Can you comment on bounds? I have 1920 MB ram allocated, server assigned default M5xxxxxxx assigments grab 1880 MB (the other core uses some for LL testing) and the M83xxxxx tests default to 1735 MB for bounds of B1=95000 and B2=1686250.

[QUOTE=PageFault;299485]This should have been harvested as low hanging fruit the first time it was factored.[/quote]That depends on the bounds involved. Which exact exponent are you referring to?

[QUOTE=PageFault;299485]Perhaps the client should do more in Stage 1 if there is insufficient ram for a good Stage 2?[/quote]It does. As a very rough guide, B2 = 20*B1 assuming normal amounts of RAM (for that range) are available, and time to run stage 2 is roughly equal to the time to run stage 1. The process of finding which bounds to use is the balance between probability of factor vs runtime. Using very rough numbers, a stage1+2 P-1 run will give you about 6% chance of factor; a stage1-only around 4% chance. Of course, this means that stage1 of stage1-only will run approx 50% longer than the stage1 part of 1+2, therefore bounds will be 50% higher. To use an example, let's take M60,000,000:
B1=600000, B2=14375000 -> 6.00% chance of factor, 4.35GHz-days
but, if you have insufficient RAM and therefore run stage1 only, it would be something around:
B1=700000 -> 3.00% chance of factor, 2.25GHz-days
half the effort, half the chance of factor, and only slightly higher B1 than normal.

[QUOTE=PageFault;299485]What I observed was a factor with B1=95000; the data on your page indicated B1=65000 for the first run.[/quote]Tell me which exponent you're talking about and I can comment further.

[QUOTE=PageFault;299485]I'll continue doing my range and I may try a hundred or so using the Pminus1 argument. Can you comment on bounds?[/QUOTE]My comment on bounds: let Prime95 do its thing. Its a complex process to select optimal bounds (which I have glossed over above), and setting them manually without a [i]very[/i] specific reason almost always results in worse bounds selection than letting Prime95 figure it out.

Another thing to think about with the bounds, a lot of times a machine that had too little memory will run a P-1 with a higher B1 than would be used by default. I had several B1=B2 exp that I had to run as Pminus1 since primenet will give no credit if my B1< the last run B1 even if I have a B2 that is 10x the old B1.

On a FYI point, the 7M to 8M(+?) range also seems to have been during a possible 'not up to snuff' programming time, since there are a fair number of factors found that should have been caught before. I even found one factor that was missed by both P-1 and TF when originally checked.

[QUOTE=bcp19;299501]the 7M to 8M(+?) range also seems to have been during a possible 'not up to snuff' programming time[/QUOTE]I know the issue exists, what's not clear is whether the problem lies with a) factors being found but not reported correctly; b) factors found and reported but not stored correctly and/or lost over time; c) bad code in Prime95 not finding factors it should. I know I've found a dozen such factors myself.

The exponent in question is M8360353.

I'm planning to fire up another batch in a week or so. I'll do a few hundred or so and we shall see the results.

There is another observation. M57078733 just started its run and (as normal) the client prints "Using Pentium4 Type-0 FFT length 3M, Pass1=768, Pass2=4K". For the M83xxxxx it used a Core2 FFT (details were not recorded). Of course, if a particular code path is faster, the client should check and use the best one. I'm wondering if anyone else has seen this behavior.

[QUOTE=James Heinrich;299493]That depends on the bounds involved. Which exact exponent are you referring to?

It does. As a very rough guide, B2 = 20*B1 assuming normal amounts of RAM (for that range) are available, and time to run stage 2 is roughly equal to the time to run stage 1. The process of finding which bounds to use is the balance between probability of factor vs runtime. Using very rough numbers, a stage1+2 P-1 run will give you about 6% chance of factor; a stage1-only around 4% chance. Of course, this means that stage1 of stage1-only will run approx 50% longer than the stage1 part of 1+2, therefore bounds will be 50% higher. To use an example, let's take M60,000,000:
B1=600000, B2=14375000 -> 6.00% chance of factor, 4.35GHz-days
but, if you have insufficient RAM and therefore run stage1 only, it would be something around:
B1=700000 -> 3.00% chance of factor, 2.25GHz-days
half the effort, half the chance of factor, and only slightly higher B1 than normal.

Tell me which exponent you're talking about and I can comment further.

[/QUOTE]

[QUOTE=PageFault;299503]The exponent in question is M8360353[/QUOTE]That factor is one of those that [i]bcp19[/i] mentioned: that factor should have been found with [url=http://mersenne-aries.sili.net/M8360353]the original P-1 bounds[/url], and can be found in stage1 with a B1 >= 63059 (or stage 2 with B1>= 4073 and B2 >= 63059). [i]Should've[/i] been found, maybe it was, but the record was lost for whatever reason, as mentioned above between me and [i]bcp19[/i].

If you submit your results.txt to the site you'll see how the bounds overlap between the original P-1 and your more recent one that (re-)found the factor. Unfortuantely PrimeNet throws away the data on what bounds were used when a P-1 factor is found so I can't graph that data without the user submitting the results for F-PM1 results.

[QUOTE=PageFault;299503]There is another observation. M57078733 just started its run and (as normal) the client prints "Using Pentium4 Type-0 FFT length 3M, Pass1=768, Pass2=4K". For the M83xxxxx it used a Core2 FFT (details were not recorded). Of course, if a particular code path is faster, the client should check and use the best one. I'm wondering if anyone else has seen this behavior.[/QUOTE]

Whenever he writes new FFTs, George times all code paths on all architectures, and chooses the fastest one regardless of what the name of the FFT is. If at low expos Core2 FFTs are chosen, that means they are faster than the Pentium4 FFTs, even on a PentiumD (which is, as I recall, what you are using).

[QUOTE=James Heinrich;280785]Found one more (bold), but this time in another range:
[url=http://mersenne-aries.sili.net/6802123]M6,802,123[/url], [url=http://mersenne-aries.sili.net/6853937]M6,853,937[/url], [url=http://mersenne-aries.sili.net/6853967]M6,853,967[/url], [url=http://mersenne-aries.sili.net/6854297]M6,854,297[/url], [url=http://mersenne-aries.sili.net/6888719]M6,888,719[/url], [url=http://mersenne-aries.sili.net/6935129]M6,935,129[/url], [url=http://mersenne-aries.sili.net/6937501]M6,937,501[/url], [b][url=http://mersenne-aries.sili.net/8855257]M8,855,257[/url][/b][/QUOTE]

Found another one for your list: [url=http://http://mersenne-aries.sili.net/exponent.php?exponentdetails=9914951]9,914,951[/url]

[QUOTE=harlee;299704]Found another one for your list: [url=http://http://mersenne-aries.sili.net/exponent.php?exponentdetails=9914951]9,914,951[/url][/QUOTE]There's now a proper list on the site: [url]http://mersenne-aries.sili.net/p1missed.php[/url]

[QUOTE=harlee;299704]Found another one for your list: [URL="http://http://mersenne-aries.sili.net/exponent.php?exponentdetails=9914951"]9,914,951[/URL][/QUOTE]
your link says [URL]http://http//[/URL]

[QUOTE=James Heinrich;299705]There's now a proper list on the site: [URL]http://mersenne-aries.sili.net/p1missed.php[/URL][/QUOTE]

This list show quite a lot of NF-PM1 entries, also from the recent past. For example:
[URL]http://mersenne-aries.sili.net/exponent.php?factordetails=1043639[/URL]
[URL]http://mersenne-aries.sili.net/exponent.php?factordetails=2000807[/URL]
[URL="http://mersenne-aries.sili.net/exponent.php?factordetails=1845568908774222013799"]http://mersenne-aries.sili.net/exponent.php?factordetails=18455[/URL]
[URL="http://mersenne-aries.sili.net/exponent.php?factordetails=1845568908774222013799"]http://mersenne-aries.sili.net/exponent.php?factordetails=445651137737144960137768908774222013799[/URL]
[URL]http://mersenne-aries.sili.net/exponent.php?factordetails=7411839124463[/URL]

Is there a problem in prime95 finding some of the factors if some special conditions occur (which?)?


On the other hand, James, could you also scan your factor repository for factors found by P-1 that should have been found by TF, but have been reported NF? If there are any, this could be used to reveal corner-case problems in mfakto/mfaktc.

[QUOTE=Bdot;299771]This list show quite a lot of NF-PM1 entries, also from the recent past.
Is there a problem in prime95 finding some of the factors if some special conditions occur (which?)?[/quote]The only "problem" in this case is that the factors were already known, and put into the "known factors" list of the Pminus1= worktodo line so that Prime95 won't break out after re-finding these known factors in stage1, but continue to run to the bounds you set. Not something that most users will ever do or know about, but a few people have fun playing around with such things.

I have adjusted the logic generating that page to exclude any factor that was already known before the P-1 test was run, and it works better now.

[QUOTE=James Heinrich;299774]The only "problem" in this case is that the factors were already known, and put into the "known factors" list of the Pminus1= worktodo line so that Prime95 won't break out after re-finding these known factors in stage1, but continue to run to the bounds you set. Not something that most users will ever do or know about, but a few people have fun playing around with such things.

I have adjusted the logic generating that page to exclude any factor that was already known before the P-1 test was run, and it works better now.[/QUOTE]

Thanks, this also cut the list in half ...

[QUOTE=harlee;299704]Found another one for your list: [URL="http://http://mersenne-aries.sili.net/exponent.php?exponentdetails=9914951"]9,914,951[/URL][/QUOTE]
[QUOTE=bcp19;299711]your link says [URL]http://http//[/URL][/QUOTE]
Corrected link: [URL="http://www.mersenne-aries.sili.net/exponent.php?exponentdetails=9914951"]9,914,951[/URL]

Another one nailed in Stage 1:

[CODE][Sat May 19 17:23:16 2012]
P-1 found a factor in stage #1, B1=610000.
UID: PageFault/boxen_01, M57111113 has a factor: 46695916625813440426631, AID: [/CODE]

I had a feeling this one had a factor ... brainfart maybe, or too much whisky ... all those 111's ...

Lets see about a range I grabbed by manual means around M70000000. Much slower, but I got tight groups of nearby exponents. I like those, in the past I used to game on blocks of factor rich exponents ... let's see what I find.

can't get P-1 work in 45.xxx.xxx to 51.xxx.xxx range?
 

Any particular reason why P-1 manual assignments in the 45.xxx.xxx to 51.xxx.xxx range are not available?

Without specifying an exponent range, I got P-1 assignments between 52.9xx.xxx and 56.2xx.xxx (two sets of 5 assignments).

When exponent range 44.000.000 to 45.999.999 specified, I got response "No large Mersenne P-1 factoring assignments found." and double-check assignments (another 5 assignments).

There would seem to be plenty of assignments in the requested range (scroll right to "Available").
[CODE]
PrimeNet Activity Summary 2012-05-28 02:00 UTC

----------=-----=-- | -----=-----=-----=-----=----- | -----=-----=-----=----- | -----=-----=-----=----- |
Exponent Range | Composite | Status Unproven | Assigned | Available |
Start Count P | F LL-D | LL LLERR NO-LL | TF P-1 LL LL-D | TF P-1 LL LL-D |
----------=-----=-- | -----=-----=-----=-----=----- | -----=-----=-----=----- | -----=-----=-----=----- |

40000000 57102 | 35705 470 20922 5 | 44 4 | 20879 |
41000000 56864 | 35539 348 20970 7 | 66 | 20911 |
42000000 56915 1 | 35693 314 20889 2 16 | 62 4 | 20841 |
43000000 56849 1 | 35507 338 20959 1 43 | 1 1 80 26 | 20895 |
44000000 56776 | 35867 308 20422 4 175 | 10 326 220 38 | 20010 |
45000000 56893 | 35795 236 20083 43 736 | 561 818 2 | 915 18569 |
46000000 56640 | 35537 229 19732 48 1094 | 1 1153 32 | 1057 18623 |
47000000 56451 | 35528 162 19217 49 1495 | 1 1564 1 | 1290 17905 |
48000000 56387 | 35473 212 18161 119 2422 | 11 2563 4 | 1930 16198 |
49000000 56603 | 35800 713 16482 264 3344 | 8 3597 2 | 514 30 15938 |

50000000 56360 | 35758 94 16241 83 4184 | 31 1 4207 6 | 82 47 16136 |
51000000 56349 | 36142 62 12932 107 7106 | 14 3 7147 | 7 63 12916 |
52000000 56209 | 35844 28 11605 77 8655 | 125 50 8392 | 27 181 11569 |
53000000 56151 | 35996 29 8175 84 11867 | 97 2 11693 | 4 195 8168 |
54000000 55997 | 35800 12 6320 54 13811 | 3464 159 9937 | 89 321 6227 |
55000000 56130 | 35636 7 4561 24 15902 | 6327 501 9108 | 81 27 4475 |
56000000 56105 | 35338 6 4290 34 16437 | 5301 651 10433 | 108 82 4192 |
57000000 55901 | 35138 1 2174 19 18569 | 7286 421 10918 | 1 49 16 2082 |
58000000 55978 | 34898 3 1386 55 19636 | 7457 357 11708 | 277 33 1277 |
59000000 55801 | 34552 136 1 21112 | 4241 55 2298 | 14400 134 135 |

[/CODE]

[QUOTE=S34960zz;300460]
There would seem to be plenty of assignments in the requested range [/QUOTE]

I think those P-1 assignments are only needed for double-checking. The server currently hands out P-1 assignments for exponents needing a first-time LL test.

I just found a triple-factor with P-1. I thought it would be too good to be true to find a 202-bit P-1 factor and assumed it was composite, but I haven't found any (previously-unknown) triple factors with P-1 before; I expected it was a pair of factors. Interestingly this is one of those exponents where the original P-1 missed one of the factors for whatever reason, but my second run at it found that one, plus another two. :smile:
[url]http://mersenne-aries.sili.net/M8724319[/url][code][Sun May 27 22:31:10 2012]
P-1 found a factor in stage #2, B1=160000, B2=3560000.
UID: JamesHeinrich/i7-920, M8724319 has a factor: 9893948425753647218051318141410341116826278223498667572999089[/code]

[QUOTE=James Heinrich;300528]I just found a triple-factor with P-1.[/QUOTE]
Cool!

I'm just curious as to what is done with a number once it has a factor or more than one in the case of the one James Heinrich found. Is it just kept for information sake or some other purpose? I know we need to figure all these factors out to search for the Mersenne Primes, but as I'm stupid when it comes to anything above basic algebra, I was wondering.

Generally once a factor is found the number is left alone. Some enterprising individuals try and find more factors (up to [url=http://mersenne-aries.sili.net/manyfactors.php]10 factors are known[/url] for some exponents), but a single factor is certainly sufficient to prove that a Mersenne number is not-prime, which is helpful towards GIMPS' goal. Ideally it would be nice to have complete factorizations of all Mersenne numbers, but since that's an unattainable goal a list of known factors will always be maintained somewhere.

Factors are great in that they're easily-verifiable proof that said Mersenne number is not prime. Lucas-Lehmer tests are great, but non-trivial to verify. There's always the very-small possibility that a supposedly not-prime result is in fact incorrect, either through error or malice, so having a factor as not-prime proof is always best. Multiple factors, while possibly interesting, don't add any extra benefit to GIMPS' goal in that sense.

[QUOTE=James Heinrich;300722](up to [url=http://mersenne-aries.sili.net/manyfactors.php]10 factors are known[/url] for some exponents)[/QUOTE]

Heh, I wonder how many exponents have factors with k==1?

[QUOTE=Dubslow;300728]Heh, I wonder how many exponents have factors with k==1?[/QUOTE]2,157,779

As it happens I spent the last 24 hours reworking my database to store k differently, so I can easily tell you.

If you care for the more detailed breakdown:[code] [total] => 2157779
[known_factors_000] => 28090
[known_factors_001] => 23476
[known_factors_002] => 21762
[known_factors_003] => 21088
[known_factors_004] => 20428
[known_factors_005] => 19978
[known_factors_006] => 19756
[known_factors_007] => 19218
[known_factors_008] => 19038
[known_factors_009] => 18865
[known_factors_010] => 18564
[known_factors_011] => 18459
[known_factors_012] => 18452
[known_factors_013] => 18238
[known_factors_014] => 18116
[known_factors_015] => 17942
[known_factors_016] => 17861
[known_factors_017] => 17662
[known_factors_018] => 17459
[known_factors_019] => 17618
[known_factors_020] => 17339
[known_factors_021] => 17209
[known_factors_022] => 17046
[known_factors_023] => 17312
[known_factors_024] => 17057
[known_factors_025] => 17046
[known_factors_026] => 16969
[known_factors_027] => 16762
[known_factors_028] => 16700
[known_factors_029] => 16913
[known_factors_030] => 16644
[known_factors_031] => 16702
[known_factors_032] => 16731
[known_factors_033] => 16655
[known_factors_034] => 16801
[known_factors_035] => 16524
[known_factors_036] => 16297
[known_factors_037] => 16428
[known_factors_038] => 16398
[known_factors_039] => 16248
[known_factors_040] => 16254
[known_factors_041] => 15932
[known_factors_042] => 16103
[known_factors_043] => 16240
[known_factors_044] => 16168
[known_factors_045] => 16150
[known_factors_046] => 15994
[known_factors_047] => 15939
[known_factors_048] => 16193
[known_factors_049] => 15844
[known_factors_050] => 15879
[known_factors_051] => 15959
[known_factors_052] => 16040
[known_factors_053] => 15870
[known_factors_054] => 15908
[known_factors_055] => 15780
[known_factors_056] => 15717
[known_factors_057] => 15743
[known_factors_058] => 15441
[known_factors_059] => 15485
[known_factors_060] => 15793
[known_factors_061] => 15599
[known_factors_062] => 15468
[known_factors_063] => 15666
[known_factors_064] => 15460
[known_factors_065] => 15399
[known_factors_066] => 15492
[known_factors_067] => 15516
[known_factors_068] => 15487
[known_factors_069] => 15470
[known_factors_070] => 15395
[known_factors_071] => 15445
[known_factors_072] => 15440
[known_factors_073] => 15346
[known_factors_074] => 15217
[known_factors_075] => 15329
[known_factors_076] => 15291
[known_factors_077] => 15182
[known_factors_078] => 15231
[known_factors_079] => 15289
[known_factors_080] => 15124
[known_factors_081] => 15219
[known_factors_082] => 15143
[known_factors_083] => 15136
[known_factors_084] => 15119
[known_factors_085] => 15289
[known_factors_086] => 15002
[known_factors_087] => 15128
[known_factors_088] => 15087
[known_factors_089] => 14987
[known_factors_090] => 14859
[known_factors_091] => 14965
[known_factors_092] => 15000
[known_factors_093] => 14888
[known_factors_094] => 14934
[known_factors_095] => 15069
[known_factors_096] => 14923
[known_factors_097] => 14955
[known_factors_098] => 14963
[known_factors_099] => 14805
[known_factors_OBD] => 502179[/code]Where "000" = 0M-10M, "001" = 10M-20M .. "099" = 990M-1000M, and OBD is >=1000M

This means approx 5% of all known factors have k=1 ... except for >=1000M where that number jumps to 62%

Law of small number? not enough tested?

Above 1000M testing is scattered (and I almost certainly don't have a complete set of either status or known factors), but the testing has been done is all very-low-level (relative to the exponent size) TF. Once GPU-to-172 gets there, and some P-1 is done, etc, then I'm sure it'll fall back to the normal ~5%.

[QUOTE=James Heinrich;300741]2,157,779

As it happens I spent the last 24 hours reworking my database to store k differently, so I can easily tell you.

<...snip...>

This means approx 5% of all known factors have k=1 ... except for >=1000M where that number jumps to 62%[/QUOTE]

You don't need very laborious calculus or database for this. Let p be a prime, a prime factor q of Mp can be of the form q=2*p+1 if and only if p is 4x+3. If p=4x+1, the smallest possible factor is 6*p+1, therefore k=3. Very easy to prove if you consider that all the factors are either 1 (mod 8) - and in this case all are 8zp+1, z>0 - either 7 (mod 8), and in this case they are 8zp+2p+1, z>=0, for p=3 (mod4) or 8zp+6p+1 for p=1 (mod 4). [B]THIS CASE [/B](when p=1 mod 4 and k=3)[B] would be somehow interesting[/B] to "enumerate" from your data base, as we have no criterion for finding it out by calculus. For the case in discussion, k=1, p can only be 3 mod 4, and [B]any enumeration [/B](searching the data base and counting the factors)[B] makes no sense[/B]: we have the Sophie-Germain criterion.

You can enumerate all the primes p=3 (mod4) for which q=2p+1 is prime up to any number you like (not only GIMPS limit of 10^9) using pari/gp in very short time. I had done this long ago, still have the work. This is the "kernel" routine, it outputs in a file all the exponents and its smallest factor.

[CODE]elimSGp3m4(start,stop,file,pflag)=
{
my(p,d,cnt);
p=max(start,5);
cnt=0;
while(p<stop,
until(p%4==3 && isprime(d=2*p+1),
p=nextprime(p+1)
);
if(p<stop,
if(bitand(pflag,1), printf("...%d...%c",p,13));
if(bitand(pflag,2), print("M"p" is divisible by "d));
if(bitand(pflag,4), write(file,p,",",d));
cnt++
)
);
return(cnt)
};
[/CODE]some sample of result:

[CODE]gp >\r tfm
gp > elimSGp3m4(0,1000,"sophie_germain_primes.txt",7)
M11 is divisible by 23
M23 is divisible by 47
M83 is divisible by 167
M131 is divisible by 263
M179 is divisible by 359
M191 is divisible by 383
M239 is divisible by 479
M251 is divisible by 503
M359 is divisible by 719
M419 is divisible by 839
M431 is divisible by 863
M443 is divisible by 887
M491 is divisible by 983
M659 is divisible by 1319
M683 is divisible by 1367
M719 is divisible by 1439
M743 is divisible by 1487
M911 is divisible by 1823
%111 = 18[/CODE]and the associated output file:
[CODE]11,23
23,47
83,167
131,263
179,359
191,383
239,479
251,503
359,719
419,839
431,863
443,887
491,983
659,1319
683,1367
719,1439
743,1487
911,1823[/CODE]which can be further used to eliminate the exponents from the list of the prime candidates. I believe this is the first things GIMPS ever did in its life.

For the record, there are 1655600 such exponents for which k of the first factor is 1, on whole the GIMPS range (under 10^9).

[CODE]gp > total=0; for(i=2,12,print("Between 10^"i-1" and 10^"i" : "cnt=elimSGp3m4(10^(i-1),10^i,,1)".\tTotal : "total+=cnt))
Between 10^1 and 10^2 : 3. Total : 3
Between 10^2 and 10^3 : 15. Total : 18
Between 10^3 and 10^4 : 81. Total : 99
Between 10^4 and 10^5 : 481. Total : 580
Between 10^5 and 10^6 : 3331. Total : 3911
Between 10^6 and 10^7 : 24179. Total : 28090
Between 10^7 and 10^8 : 183609. Total : 211699
Between 10^8 and 10^9 : 1443901. Total : 1655600
...1302645131...[/CODE](still running, it will take about 5 minutes to reach here, maybe 50 minutes or a hour or so to reach 10Gig, it can still be optimized, but who needs all this statistics? :razz:)

[QUOTE=James Heinrich;300746]Above 1000M testing is scattered (and I almost certainly don't have a complete set of either status or known factors), but the testing has been done is all very-low-level (relative to the exponent size) TF. Once GPU-to-172 gets there, and some P-1 is done, etc, then I'm sure it'll fall back to the normal ~5%.[/QUOTE]
I have/had a complete list of factors under 2^56 of Mp for all prime exponents p between 0 and 10G. This is generated by hunting for the size of the factor first (for a given prime q which is 1 or 7 mod 8, factor (q-1)/2 and see if for any p in the resulted factor list, if q divides Mp. This can be done very fast, as you are not interested in full-factoring q-1, but only in its factors p which are on your "interest range", in our case, lower then a billion, or 10 billions). This idea is debated on the forum here and there in the past, and I even posted pieces of (unoptimized) pari code. I did this long time ago, I may not find all the files, but if you are interested I can send you the log files which I still can find. It takes one day to go to 2^40 on a single core, then the time doubles for each bit. It generates different files for each exponent range and bit range. See here a starting-from-40-bits-factors interrupted after about 30 seconds, and then a second run for starting-from-45-bits factors, interrupted after about 5 minutes (of course, for higher bit-count the factors are output less and less frequent). For 50 bits and higher, one can get about ONE factor every few minutes. In the files it creates, the format is "factor, exponent". If you are really interested, I can look for the original (complete) files, or eventually give it a new run, but this would take some time. The only thing I found interesting at the time when I was doing this it was the fact that the factors come "in waves", for example you see even for the interval I have run this simple demo, there is no file with _9B_, this means there is no factor of Mp with exponent p between 9G and 10G ("B" stands for billion, but I use G for Giga to avoid confusion, as some people use long scale, B=10^12, other use short scale, B=10^9). The factors coming in waves, in packages, buckets, whatever, is somehow normal, due to the form of the factors. As k in q=2kp+1 can never be of the form 4x+2 (a factor can't be, for example 4p+1, 12p+1, 20p+1, etc, as those would be all 5 mod 8, and we know the factors have to be 1 or 7 mod 8), there will be "gaps", behaving almost the same as prime gaps. For example, if p is between 1000 and 2000, all factors 2p+1 would be in 2000-4000, all of the form 6p+1 would be in 6000-12000, and there would never be a factor between 4000 and 6000. If p is in 6000-7000, then by the same reason, there could never be a factor below 12000, nor between 14-36 thousands, nor between 42-48 thousands, 56-60, 70-84, and nor 126-132 thousands. This can be scaled to millions, billions or trillions. As the interval grows, there are more and larger gaps. But more than this, one can not get. There is no known way one could predict where a factor will be, or what values k will take for a certain exponent or range of exponents.

[QUOTE=James Heinrich;300528]I just found a triple-factor with P-1.[/QUOTE]Another slightly unusual composite P-1 factor:
[url]http://mersenne-aries.sili.net/M8724929[/url]
[code][Wed Jun 13 17:30:01 2012]
P-1 found a factor in stage #2, B1=160000, B2=3560000.
UID: JamesHeinrich/i7-920, M8724929 has a factor: 2929655011230723414437969299453013510477993453298031[/code]Only 171 bits this time, but one of the components was still a respectable 105 bits, and the other 65-bit factor was just slightly outside the normal B2 range, so Brent-Suyama saved the day.

Might be a nice idea to move those tf levels up a bit at some point. Should be dead easy with a gpu.

[QUOTE=henryzz;302686]Might be a nice idea to move those tf levels up a bit at some point. Should be dead easy with a gpu.[/QUOTE]
Not with Chalsall at the helm though.

[QUOTE=davieddy;302688]Not with Chalsall at the helm though.[/QUOTE]

Please, can't you shut up for once?!

useless ?
P-1 found a factor in stage #2, B1=105000, B2=1916250.
UID: firejuggler, M8857483 has a factor: 91969736105950565521,

[QUOTE=kracker;302765]Please, can't you shut up for once?![/QUOTE]

I agree. As far as I can tell you offer nothing worthwhile to the project. Especially when compared to what Chris has done.

[QUOTE=KyleAskine;302769]I agree. As far as I can tell you offer nothing worthwhile to the project. Especially when compared to what Chris has done.[/QUOTE]

Thanks guys. But don't sweat it.

Those who can't, talk.... :wink:

Helpful link for restoring sanity:
[url]http://www.mersenneforum.org/profile.php?do=ignorelist[/url]


[QUOTE=firejuggler;302768]useless ?
P-1 found a factor in stage #2, B1=105000, B2=1916250.
UID: firejuggler, M8857483 has a factor: 91969736105950565521,[/QUOTE]Useless how?

well it's an double checked exponent in the very low range.

[QUOTE=firejuggler;302773]well it's an double checked exponent in the very low range.[/QUOTE]Was the factor previously known? If not then it's useful. I've found hundreds of such factors myself, as have many others here.

[QUOTE=James Heinrich;302779]Was the factor previously known? If not then it's useful. I've found hundreds of such factors myself, as have many others here.[/QUOTE]

And we all send our new found factors to Will Edgington...

Luigi

[QUOTE=ET_;302796]And we all send our new found factors to Will Edgington...

Luigi[/QUOTE]
We do?

[QUOTE=ET_;302796]And we all send our new found factors to Will Edgington...[/QUOTE]Oh? I don't think most of us knew we did... :unsure:

[QUOTE=KyleAskine;302769]I agree. As far as I can tell you offer nothing worthwhile to the project. Especially when compared to what Chris has done.[/QUOTE]

[QUOTE=chalsall;302770]Thanks guys. But don't sweat it.

Those who can't, talk.... :wink:[/QUOTE]
Enough of your mindless insolence already

I found a 167.9 bit composite factor: [URL]http://mersenne-aries.sili.net/exponent.php?exponentdetails=8414383[/URL]

WoW.. nice one

[QUOTE=firejuggler;303578]WoW.. nice one[/QUOTE]

I'd say "nice two!"

Luigi

Not too long ago, a few people explained to me the percentages between stage 1 and stage 2 of P-1 how factors are found. Knowing that, and maybe it is all just a coincidence, I am surprised because I have found 3 factors of numbers just today when all the time before I would go days between finding just one. Considering the percentage chance of finding a factor that is on screen when a new P-1 starts, it makes me kinda wonder how I could just have this much "good luck".

You can wonder why you did have so few hit before, too.

[QUOTE=Jwb52z;303612]Not too long ago, a few people explained to me the percentages between stage 1 and stage 2 of P-1 how factors are found. Knowing that, and maybe it is all just a coincidence, I am surprised because I have found 3 factors of numbers just today when all the time before I would go days between finding just one. Considering the percentage chance of finding a factor that is on screen when a new P-1 starts, it makes me kinda wonder how I could just have this much "good luck".[/QUOTE]Sometimes we look for a causative factor behind random occurrences when they seem not random-enough.

Such pattern-seeking is useful when there occasionally are nonrandom factors (e.g., there really is a tiger lurking in those shadows), where there can be a severe penalty for not suspecting nonrandomness and acting on that suspicion, but there are no tigers lurking in factors of Mersenne numbers.

1st composite factor
 

Found my 1st composite factor today:

[Sat Jun 30 05:48:13 2012]
P-1 found a factor in stage #1, B1=555000.
UID: flashjh/P1Main, [URL="http://mersenne-aries.sili.net/exponent.php?exponentdetails=55695851"]M55695851[/URL] has a factor: 5177355259441074001675920029884672048668915182092512593

bits: 181.756

[QUOTE=flashjh;303747]Found my 1st composite factor today:
bits: 181.756[/QUOTE]Nice. Both in stage-1 too.

How do you know how many bits a factor you find is equivalent? I haven't seen that printed on the results anywhere.

[QUOTE=Jwb52z;303763]How do you know how many bits a factor you find is equivalent? I haven't seen that printed on the results anywhere.[/QUOTE]

If you follow the link in my post to James' site you'll see that it displays all the info you're looking for there.

That's an awesome find. The k of the first individual factor is nice and smooth. Good work!

[QUOTE=Jwb52z;303763]How do you know how many bits a factor you find is equivalent? I haven't seen that printed on the results anywhere.[/QUOTE]As [i]flashjh[/i] said any of the factor/exponent detail pages will have that info; the right-side menu of any page on my site has a box where you can put any number in to get the number of bits.

More generically: log(factor)/log(2) will give you the number of bits.

Where log() is the natural logarithm, base e. You could alternately just do log2(factor), the logarithm base 2 :razz:

[QUOTE=Dubslow;303771]Where log() is the natural logarithm, base e. You could alternately just do log2(factor), the logarithm base 2 :razz:[/QUOTE]
Does it matter? How about if log() is base 10? or 59? :razz: :razz:

[QUOTE=flashjh;303765]If you follow the link in my post to James' site you'll see that it displays all the info you're looking for there.[/QUOTE]Thank you for pointing that out to me. I found out my largest factor is just over 100 bits so far.

[url]http://mersenne-aries.sili.net/exponent.php?exponentdetails=1131113[/url] for my latest factor- one bit from TF finding instead of P-1

[QUOTE=LaurV;303782]Does it matter? How about if log() is base 10? or 59? :razz: :razz:[/QUOTE]

Yes, LaurV, it must be base 2. Base 10 would tell you how many digits it is, and base 59 would...just be stupid. Base 2 tells you how many bits. Also log2(factor) = x where 2^x=(factor)

How long does it take a factor to be listed on the page I was suggested to go to about seeing the bit length? I just found a factor and it's not there yet, so I assume it's not directly linked or instant.

[QUOTE=Jwb52z;303811]How long does it take a factor to be listed on the page I was suggested to go to about seeing the bit length? I just found a factor and it's not there yet, so I assume it's not directly linked or instant.[/QUOTE]PrimeNet posts the recent data every hour, which I grab at roughly half past each hour. So worst case about 90 minutes. Unless, of course, lots of other data was submitted that hour and more than 1000 results were recorded that hour, in which case it may fall off the PrimeNet report.

Manually submitting results.txt to [url]http://mersenne-aries.sili.net[/url] as often as you like is the best way to ensure you're seeing accurate data. That's reflected instantly, and also contains useful data that's impossible to get from PrimeNet, so manual submission is always welcome and encouraged.

[QUOTE=c10ck3r;303806]
Yes, LaurV, it must be base 2. Base 10 would tell you how many digits it is, and base 59 would...just be stupid. Base 2 tells you how many bits. Also log2(factor) = x where 2^x=(factor)[/QUOTE]
You can do it with any base b:

log2(x) = logb(x)/logb(2).

It's called the change of base formula, it's what James used with base e, and it shows that loga(x)/logb(x) is a ratio that is independent of x (it only depends on a and b).

This seems like a fairly low bit length factor I found, but what do I know?, so finding any others might be interesting:

P-1 found a factor in stage #2, B1=565000, B2=11158750.
UID: Jwb52z/Clay, M56995177 has a factor: 11399497561966901971601

73.271 bits.

Yes, it is fairly low. A few bits lower and TF would have found it first.

[QUOTE=c10ck3r;303806]
Yes, LaurV, it must be base 2. Base 10 would tell you how many digits it is, and base 59 would...just be stupid. Base 2 tells you how many bits. Also log2(factor) = x where 2^x=(factor)[/QUOTE]
[strike]I hope your post was a joke. I was not arguing about log2() formula, but about log() formula. That is my "any base" against Dubslow's "base e".
How about you read my post again and THINK about it...[/strike]

edit: crosspost, saw the next (current) page where Dubslow answered already.

LaurV, I was under the impression that your question was about the second half of Dubslow's post, not the first. For the first part, yes, it could be any base. He never said the first part was base 2, but instead base e, even though JH's generic formula is assumed to be base 10 without the presence of a listed base. If, as Dubslow suggested, log() was the natural logarithm, it would have been written ln().
Clarification- its a beautiful thing!

[QUOTE=c10ck3r;303835]If, as Dubslow suggested, log() was the natural logarithm, it would have been written ln().[/QUOTE]

Not always. In fact, not often.

In Perl, C, C++ and many, many other languages, log() returns the "natural logarithm". ln() doesn't exist.

As James then pointed out, log(x)/log(base) will give you the number of digits in whatever base you desire. And, thus, you can create any of the other "log" functions using this formula.

[QUOTE=c10ck3r;303835]Clarification- its a beautiful thing![/QUOTE]

Indeed. :smile:

log() meaning base ten or base e depends on who you ask and when. If you ask me when I'm writing out calculus by hand, I'll use ln() because it's shorter.

Wolfram Alpha generally assumes base e for log(), and uses log() for base e when displaying things.

:smile: