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Old 2003-05-13, 15:52   #1
wblipp
 
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Default New factor of M(5040) - who to tell?

Using non-GIMPS 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?
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Old 2003-05-13, 17:13   #2
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Default 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.
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Old 2003-05-13, 17:32   #3
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Default Re: reporting factors

Quote:
Originally Posted by philmoore
Congratulations! What was your factoring method?
Ummm - it's a bit embarassing. I was using Dario Alejandro Alpern's Java ECM at http://www.alpertron.com.ar/ECM.HTM. It's not an efficient way to find new factors, but I wasn't really on a quest for new factors. This popped out while I was working on something else and thought it should be shared.
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Old 2003-05-13, 18:10   #4
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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 349-digit composite which might be more efficient. But probably GMP-ECM 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!
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Old 2003-05-13, 18:44   #5
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Quote:
Originally Posted by philmoore
But probably GMP-ECM is the most efficient publicly available software right now for a number of general form.
I'm without a C compiler at present, and the only download I've seen for GMP-ECM is for the source code. Is there a downloadable Windows executable someplace?
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Old 2003-05-13, 19:51   #6
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The ECM-net page lists the following resource for binaries, thanks to Torbjo"rn Granlund:

ftp://ftp.swox.com/private/tege/gmp-ecm/

I haven't checked them out, however.
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Old 2003-05-13, 23:39   #7
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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 2^2520-1. 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 2^5040-1 by above factors.
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Old 2003-05-14, 04:35   #8
jocelynl
 
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Here is what I get for (2^5040-1) divided by your factors.

[code:1] 1502295864217530495646381863089376753296711058354680590384314405709393045604732
28112749569393806128851400002429238891544737815331236586653515563082204345446869
52908285949591439980287822417648543086547306560964446133955493946057624119809028
31632294301408944977247508100484773145446401134864608304571556675740867193982359
81802112734328174682899172971628159548376133022523497371234276420750501259004309
08721033330653913374596700343306284362325640981598351563802259458774833242581768
2281108360881
[/code:1]
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Old 2003-05-14, 07:40   #9
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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.
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Old 2003-05-14, 08:27   #10
smh
 
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Quote:
Originally Posted by jocelynl
Here is what I get for (2^5040-1) divided by your factors.

[code:1] 1502295864217530495646381863089376753296711058354680590384314405709393045604732
28112749569393806128851400002429238891544737815331236586653515563082204345446869
52908285949591439980287822417648543086547306560964446133955493946057624119809028
31632294301408944977247508100484773145446401134864608304571556675740867193982359
81802112734328174682899172971628159548376133022523497371234276420750501259004309
08721033330653913374596700343306284362325640981598351563802259458774833242581768
2281108360881
[/code:1]
Thanks,

I missed 1 factor for 2^2520-1 (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:
Originally Posted by pakaran
Smh, those factors are probably small enough to certify with Primo
Yes they are small enough to certify with primo (or other tools), but it was 1:30 AM and i didn't feel like doing it at that time.
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Old 2003-05-14, 09:19   #11
smh
 
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Hmm, getting a little confused now.

I just tried Dario Alpern's ECM applet to factor (2^5040-1)/(2^2520-1)

It quickly leaves the C347 composite. With wblipp's factor this leaves the C324. But 2^2520-1 also isn't completely factored yet. Still 147 digits to go (LowM.txt confirms this). So together 2^5040-1 is almost 500 digits short of it's complete factorization. Or is there any flaw in my thinking?

Sander
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