20090120, 18:28  #1 
Apr 2007
Spessart/Germany
2·3^{4} Posts 
Missing factors at the 'Known Factors' page
Hello,
today I got a litttle bit trouble because at the 'Known Factors' page not all factors are listet. F.e. for M2251 there is only 1 factor listet. I put M2251 to my prptest proggy, divided out this factor and got: the remaining cofactor is still composite. The Alpertron said it, too (I forgot at that moment that the Alpertron does not ask for known factors of the number from the server, if one factor is given already). I run some small ECMcurves with prime95 and 'found' 2 factors. Then I became startled and asked the Alpertron again only for M2251 and soon I got all factors. I stopped the curves running with prime95, but some are reportet as: pnErrorResult=40 pnErrorDetail=Factor 1687942505818611032423917201 reported for completely factored M2251 Thus I have 2 questions: why are not all known factors listet at the status pages? can I be sure that at least those numbers with remaining composite cofactor have all known factors listet at the status pages? best regards, Matthias 
20090120, 18:50  #2 
Jun 2003
7·167 Posts 
Presumably the cofactors left after all the known small factors are divided out are not listed because they can be easily generated in any particular case, and storing them all would be prohibitive. Many of them will be tens of millions of digits long.

20090120, 19:01  #3  
Apr 2007
Spessart/Germany
2×3^{4} Posts 
Quote:
p6 778847 p26 17620954939878356226435007 p34 1687942505818611032423917201 only this factor is listet: p6 400679 the remainig cofactor of M2251 after dividing out these 4 factors is a p614 If only the first factor of completely factored Mersennenumber is listet, then at least a hint about 'completely factored' is needed at the 'Known Factors' page (and the 'Exponent Status' page). best regards, Matthias 

20090120, 19:25  #4 
Jun 2008
48_{16} Posts 
The goal of GIMPS is not to list factors, so why bother storing them. I guess this is just one of many cases only the smallest factor is listed. You are free to submit more, but this just isn't the place for them.
Will Edgington maintains a database with known Mersenne factors and search limits etc. http://www.garlic.com/~wedgingt/mersenne.html 
20090120, 20:09  #5 
Apr 2007
Spessart/Germany
10100010_{2} Posts 
Hello,
of course it is not GIMPS' first wish to list all factors. But the project keeps track of the ECMcurves for already factored Mnumbers at least up to exponent 10000. And to prevent myself from finding of already known factors I need to know them (that's about my second question). If a number like M2251 is already completely factored, then the project doesn't need anymore list all factors, one is enough. But then at least a hint about the status of completely factored is needed imho. Or you can get such trouble like I got. Of course I know that such an exponent is not longer listet at the ECMstatus page for Mnumbers with known factors. But I don't look always at the ECMpage. It is simply a question of time. And btw. there are listet all factors of M29, so why not of M2511. I agree that there must be a limit for the exponent for the storing of all known factors. But this limit must be at least the same as the exponent limit for the ECMcurves with known factors the server keeps track off. And to store all known factors up to exponent 10000 should not need much more space as the list provided at the moment. How I said, I don't know if there are missing known factors for not completely factored numbers. I will check it, maybe tomorrow. If yes, all who are doing ECM on these numbers will have some problems with finding already known factors. The missing known factors of completely factored Mnumbers are less a problem if there is a hint about the status in the 'Known Factors' page. Then one can be sure about the status without looking at the ECMstatus page again... best regards, Matthias edit: of course I know Edgington's tables and Wagstaff's and Brent's... but do you look every time at this tables for all known factors if you only want to run some ECMcurves at an exponent? Last fiddled with by MatWurS530113 on 20090120 at 20:12 
20090121, 01:34  #6  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}·3·641 Posts 
Quote:
Edgington's page has a link to "mersdata.zip: lowM.txt, DATABASE, DB.nf, primeM.txt, factoredM.txt, etc., zipped" I don't know whether its files are updated regularly. If they are, you could get lowm.txt there. Quote:
Quote:
Download and store a copy of the page every month or so, so you can refer to that copy quickly offline. Better yet: sign up for one of those free services that will notify you whenever a particular web page changes, so you can redownload only when it changes. Quote:
How about downloading and storing a copy of Edgington's table (or the file I mentioned above) once a month or so, whenever you do the same for the ECMstatus page? Or put it on your pagechangenotification service list. Last fiddled with by cheesehead on 20090121 at 01:57 

20090121, 03:11  #7 
P90 years forever!
Aug 2002
Yeehaw, FL
7·1,021 Posts 
Thanks. Let me know if you find other factors missing from the database.

20090121, 16:58  #8 
Apr 2007
Spessart/Germany
242_{8} Posts 
Hello,
cheesehead, I will come back to your answer, but atm I have some other problems detectet while finding some more of these factors. I createt a list with all known factors (for exponents from 1 to 5000) from the GIMPS database and stored it to a textfile. With my own proggy I read out the exponents, createt the Mnumbers, divided out the factors and performed a prptest at the remaining cofactors. The composite cofactors I stored in a table. Then I deletet all those exponents from this table which are still at the ECMprogress page listet with known factors for ECM'ing. From the remaining exponents in the list I knew this: my proggy says that the last remaing cofactors of these exponents are still composite but the server hasn't listet them anymore at ECMpage, so the server 'thinks' or 'knows' that the last remaining cofactor is prp. It follows that there must be more factors for these exponents. I searched for them (most I got with the Alpertron, some from Brent's, some from Wagstaff's tables etc...). I attached a list with the factors I got. But there are 3 exponents I have some problem with: M857 should be deletet from the ECMpage as the last remaining cofactor is prp afaik, 2 factors were added some hours ago (nice to see such long factors found by ECM ) But the real problems are M3259 and M4729 from both numbers 1 factor is known at the GIMPSdatabase: M3259: 21926805872270062496819221124452121 M4729: 61944189981415866671112479477273 my proggy says: the remaining cofactors of these Mnumbers are still composite. They are not listet for ECM'ing with known factors, thus I have to assume the server 'thinks' or 'knows' that these cofactors are prp. But there are no more factors to find for these 2 exponents. The Alpertron makes a Rabin Miller prptest at the cofactors, I haven't finished them as they need much time. But the output of my proggy's prptest that they are composite is a statement for sure... I already run curves with B1=1e6 (changing to B1=3e6 soon) on the remaining cofactors, but I need a verification of the prptest. Are the remaining cofactors of M3259 and M4729 composite or prp? If they are composite they should be added to the ECMprogress page with known factors. If they are prp and my proggy's prptest is faulty then I will report some senseless work in a few hours. best regards, Matthias Code:
M1223 c 31799,439191833149903 M1289 c 108817410937,827446666316953,9580889333063599,16055826953448199975207 M1303 c 1140690503 M1307 c 141196558805510033914433414063,161633497146742177992711798481 M1327 c 6363071161 M1361 c 3397057,137450113,30322542339673,15459763525875943,856450061281312036458486309832227737 M1459 c 93377 M1531 c 14661821742553 M1553 c 354271470446427666439,432076532964254217618937,67625467049371226906709645391,169336513704068271013494661928987033 M1693 c 3 361912 721093432406946778492953,414073707708708359213580367115039,21637859486326546740118800926236362073 M1783 c 59767828889,21991704205191358757046463,60701317462845977755176049,1943163990190458280022304032374692151 M1997 c 2982351597692070261023,342849716969843931264330628335073 M2069 c 1816583,1662927218441,1776510807594595616100267889706057 M2311 c 4514379640917651135021865565129 M2383 c 889865441849036810633962436005361 M2447 c 2771915076094391,459390495235738452861593,24700068031700569654277801,3922634957266302331319319913 M2549 c 5490243876052618831,324013067177330948216089046508086969 M2677 c 81699346406928829474760749455463 M2699 c 307687,1187561,7570504839257,1987104667810711 M2837 c 138871151,336396730297 M2909 c 46174737359,29101424767901148287,2810063687215981074703243943 M3041 c 5565031 M3259 c ??? M3547 c 148823192092809407 M3833 c 340789152474053904109001 M4127 c 2080009 M4729 c ??? M4751 c 3274778783,629530076753,81630665742097,1507074535068001 M4871 c 144558074148074062894378117006327 
20090121, 17:34  #9  
Jun 2008
2^{3}×3^{2} Posts 
Quote:
Edgingtons factoredM.txt agrees, which indicates he has primality certificates. I guess your program contains a bug... 

20090121, 17:45  #10 
P90 years forever!
Aug 2002
Yeehaw, FL
1101111101011_{2} Posts 
Prime95 thinks the 2 are PRP:
Code:
[Jan 21 12:42] Worker starting [Jan 21 12:42] Setting affinity to run worker on any logical CPU. [Jan 21 12:42] Starting PRP test of M4729/61944189981415866671112479477273 using FFT length 224 [Jan 21 12:42] M4729/61944189981415866671112479477273 is a probable prime! Wd1: 24F224F2,00000000 [Jan 21 12:42] Starting PRP test of M3259/21926805872270062496819221124452121 using FFT length 160 [Jan 21 12:42] M3259/21926805872270062496819221124452121 is a probable prime! Wd1: 19761976,00000000 
20090121, 17:52  #11 
"Ben"
Feb 2007
2·5·7·47 Posts 
FWIW, Yafu also agrees that the cofactors are prime. It uses the RabinMiller prp test with 20 witnesses (the first 20 primes). I believe Mathematica does MR base 2 and 3, then a lucas test.

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