20030513, 15:52  #1 
"William"
May 2003
New Haven
2,371 Posts 
New factor of M(5040)  who to tell?
Using nonGIMPS tools, I've found a new factor of M(5040). The file lowM.txt shows this as having a C349 composite. The following 23 digit number is a factor, leaving a C324 Composite.
75959899466493446490241 It seem like I ought to report this to somebody so that lowM.txt can get updated, and perhaps some other data bases as well  but I haven't been able to figure out who or how. I've sent an email to Will Edgington  is there anything else I should do? 
20030513, 17:13  #2 
"Phil"
Sep 2002
Tracktown, U.S.A.
3×373 Posts 
reporting factors
Will is the right person to notify. When I sent him a factor in March, he said that he was very busy at the moment due to work demands, and he didn't know when he was going to get the file updated, but he will eventually get your factor in.
Congratulations! What was your factoring method? Mersenne numbers with composite exponents above 1200 are a rich area for factoring. I have found factors for several by Prime95 ECM. The catch is, you have to use Will's files first to edit lowm.txt for the known factors of the numbers you wish to work on. For a composite number like 5040=2^4*3^2*5*7, this involves looking at the entries in Will's files not only for 5040, but also for all 58 proper factors of 5040. 
20030513, 17:32  #3  
"William"
May 2003
New Haven
2,371 Posts 
Re: reporting factors
Quote:


20030513, 18:10  #4 
"Phil"
Sep 2002
Tracktown, U.S.A.
3×373 Posts 
Actually, Dario Alpern's Java ECM is a nice little program. Note that if you were to try to factor M5040 using Prime95 ECM, you would have to run curves on the full number with 1518 decimal digits. On the other hand, you could run Dario's program on just the 349digit composite which might be more efficient. But probably GMPECM is the most efficient publicly available software right now for a number of general form. Since you are now down to 324 digits, perhaps the next factor could finish the factorization. Or perhaps not  ECM seems to attract gamblers!

20030513, 18:44  #5  
"William"
May 2003
New Haven
2,371 Posts 
Quote:


20030513, 19:51  #6 
"Phil"
Sep 2002
Tracktown, U.S.A.
45F_{16} Posts 
The ECMnet page lists the following resource for binaries, thanks to Torbjo"rn Granlund:
ftp://ftp.swox.com/private/tege/gmpecm/ I haven't checked them out, however. 
20030513, 23:39  #7 
"Sander"
Oct 2002
52.345322,5.52471
29×41 Posts 
There are also a few binaries in the filesection of the primenumbers group on Yahoo http://groups.yahoo.com
I've been playing around with M5040 a bit. I couldn't find all factorizations online so i did this myself (might be errors in there) This are all factors below 1 million [code:1] 3^3*5^2*7^2*11*13*17*19*29*31*37*41*43*61*71*73*97*109*113* 127*151*181*211*241*257*281*331*337*421*433*577*631*673*1009* 1321*1429*2017*2521*3361*4481*5153*5419*13441*14449*21169* 23311*29191*34273*38737*54001*61681*86171*92737*106681*122921 *127681*152041*557761*649657*664441*736961*870031*983431 [/code:1] Factors below are only prp. [code:1] 1130641 1325521 1564921 1711081 1765891 2627857 7416361 8369281 15790321 18837001 29247661 47392381 269389009 394783681 430839361 755667361 4278255361 4562284561 4841172001 25629623713 40388473189 46908728641 54410972897 77158673929 88959882481 118750098349 146919792181 168692292721 487824887233 1586308510081 1041815865690181 1538595959564161 469775495062434961 1475204679190128571777 75959899466493446490241 17369459529909057773233442461 84179842077657862011867889681 29728307155963706810228435378401 54169520413224311136354324156824071681 11247702599676505481447137991664348691 15169173997557864184867895400813639018421 3421249381705368039830334190046211225116161 750016890283777055704738227247474485366338380663681 14510642956629460126286667764218111732339625499480335264478327629658324054225616417 380237945545576041143329842469322327462093080857230396812644586765650440050917813566181601 [/code:1] At this moment i haven't completely factored 2^25201. I'm left with a 168 digit composite. [code:1] 1865455415767446246211754785774969335268930237747863040913439 // 9429317498045223224625312457414649362508212370154637421333625 // 4741455635824194620181872053734055357780307761 [/code:1] At this moment i'm not able to find out whats left when you divide 2^50401 by above factors. 
20030514, 04:35  #8 
Sep 2002
2·131 Posts 
Here is what I get for (2^50401) divided by your factors.
[code:1] 1502295864217530495646381863089376753296711058354680590384314405709393045604732 28112749569393806128851400002429238891544737815331236586653515563082204345446869 52908285949591439980287822417648543086547306560964446133955493946057624119809028 31632294301408944977247508100484773145446401134864608304571556675740867193982359 81802112734328174682899172971628159548376133022523497371234276420750501259004309 08721033330653913374596700343306284362325640981598351563802259458774833242581768 2281108360881 [/code:1] 
20030514, 07:40  #9 
Aug 2002
3×83 Posts 
Smh, those factors are probably small enough to certify with Primo. Check it out at http://www.ellipsa.net. If you're in the US, I can run it for you, I have a license for his old shareware version.

20030514, 08:27  #10  
"Sander"
Oct 2002
52.345322,5.52471
29×41 Posts 
Quote:
I missed 1 factor for 2^25201 (which is in LowM.txt) [code:1]1626833408812908876721[/code:1] Which leaves: [code:1] 1146678821360484904413668631221136634750152896688149518984842 4580801853423083935498869719939119397348510170471098140181001 7793878949099579507258241[/code:1] Thats still 492 and 147 digits left. Thats by far not 324 digits. Where can i find the remaining? Quote:


20030514, 09:19  #11 
"Sander"
Oct 2002
52.345322,5.52471
29·41 Posts 
Hmm, getting a little confused now.
I just tried Dario Alpern's ECM applet to factor (2^50401)/(2^25201) It quickly leaves the C347 composite. With wblipp's factor this leaves the C324. But 2^25201 also isn't completely factored yet. Still 147 digits to go (LowM.txt confirms this). So together 2^50401 is almost 500 digits short of it's complete factorization. Or is there any flaw in my thinking? Sander 
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