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 2003-09-15, 23:03 #1 GP2     Sep 2003 22·3·5·43 Posts Biggest factors The top 20 biggest factors: Code: digits exp factor ------ --- ------ 98 727 17606291711815434037934881872331611670777491166445300472749449436575622328171096762265466521858927 69 523 160188778313202118610543685368878688932828701136501444932217468039063 66 751 227640245125324450927745881868402667694620457976381782672549806487 61 809 4148386731260605647525186547488842396461625774241327567978137 57 997 167560816514084819488737767976263150405095191554732902607 45 17504141 426315489966437174530195419710289226952407399 43 983 1808226257914551209964473260866417929207023 42 6659 226211124686120782835233945344253671049543 41 2797 21302877855270603243781956883847214766183 41 10169 10402314702094700470118039921523041260063 40 1283 4824675346114250541198242904214396192319 39 14334623 563796628294674772855559264041716715663 39 2161 117194366114889271070074059667667222873 38 1427 19054580564725546974193126830978590503 37 15864539 5811726848289439035828246985293098183 37 8521 2611675093146863713541108778540140113 37 27691 1734072082042172647364731231822850071 37 56489 1555394473900812447866858212371845927 36 20396191 275806877795314616777110237874197111 36 8831 164856377760300429239292726292199519 Presumably all the large exponents (17.5M, 14.3M, 15.8M, 20.3M) were factored using P-1. And it's known that M6659 was also factored using P-1. However, the other small exponents were probably done with ECM or other methods.
 2003-09-15, 23:09 #2 Xyzzy     "Mike" Aug 2002 7,691 Posts Boy that line wrapping is ugly...
 2003-09-15, 23:15 #3 apocalypse   Feb 2003 2·3·29 Posts I believe M997 was found with ECM, and M727 and M809 were found with NFS, but I don't know about the rest. M523 and M751 are too big to have been found with ECM (M997's factor is the current champion there) Last fiddled with by apocalypse on 2003-09-15 at 23:18
 2003-09-16, 00:24 #4 outlnder     Aug 2002 2·3·53 Posts Anyway to give credit to the person returning these factors?? It's always nice to see one's name every now and again when the Top Ten or Hundred are mentioned.
2003-09-16, 00:30   #5
Wacky

Jun 2003
The Texas Hill Country

32×112 Posts
Re: Biggest factors

Quote:
 Originally posted by GP2 The top 20 biggest factors: Code: digits exp factor ------ --- ------ 98 727 17606291711815434037934881872331611670777491166445300472749449436575622328171096762265466521858927 69 523 160188778313202118610543685368878688932828701136501444932217468039063 36 8831 164856377760300429239292726292199519
What is your criterion for "biggest factor"?

In the Cunningham tables there are many ultimate factors that are significantly larger than those listed. There are also many that have two factors larger than the 36 digits that you include in your list. For example,
Code:
4755  2,1087- c235 23864222009193938317456687011256092421563991. c192 Beesley ECMNET
4757  2, 809- c244 4148386731260605647525186547488842396461625774241327567978137. p183 Franke+Kleinjung+Montgomery snfs
4778  2, 673- c151 68396769572915971687133122358352070840260017483089158059519. p92 NFSNET"
4827  2, 773- c142 3102804258869848876949115800490112967822146918598407. p91 P. Johansson ECMNET
quickly come to mind.

2003-09-16, 01:01   #6
GP2

Sep 2003

22·3·5·43 Posts
Re: Re: Biggest factors

Quote:
 Originally posted by Wacky What is your criterion for "biggest factor"? In the Cunningham tables there are many ultimate factors that are significantly larger than those listed.
The GIMPS project simply stores one factor (almost always the smallest-known), whereas the Cunningham project tries to find the complete factorization.

I just listed the 20 biggest factors stored within the data file (FACTORS.CMP). In other, the 20 biggest smallest-known factors of Mersenne exponents.

It turns out that M673, M773, M1087 all have trivial factors, and the factor for M809 that you list is actually the same that I listed (although line wrap disguises this).

2003-09-16, 01:15   #7
GP2

Sep 2003

50248 Posts

Quote:
 Originally posted by outlnder Anyway to give credit to the person returning these factors?? It's always nice to see one's name every now and again when the Top Ten or Hundred are mentioned.
The FACTORS.CMP file contains only exponents and factors.

The Primenet server gives you credit for factoring when you return a result, but the database files don't permanently record who returned it.

It's very expensive to verify a 64-bit residue: you have to redo a full LL test. But it's trivial to verify a factor, in fact, all 2 million plus factors in the database can be verified in a couple of minutes total. So for factors, it's enough just to record just their existence, whereas with residues you want to record who returned it with what program and so forth just in case that information comes in handy later for tracking bad results.

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