Biggest factors

GP2 · 2003-09-15, 23:03

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.

Xyzzy · 2003-09-15, 23:09

Boy that line wrapping is ugly...

apocalypse · 2003-09-15, 23:15

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)

outlnder · 2003-09-16, 00:24

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.

Wacky · 2003-09-16, 00:30

Quote:

Originally posted by GP2
The top 20 biggest factors:

Code:

digits exp factor ------ --- ------ 98 727 17606291711815434037934881872331611670777491166445300472749449436575622328171096762265466521858927 69 523 160188778313202118610543685368878688932828701136501444932217468039063 <snip> 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.

GP2 · 2003-09-16, 01:01

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).

GP2 · 2003-09-16, 01:15

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.

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

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2003-09-15, 23:09	#2
Xyzzy Aug 2002 20555₈ Posts	Boy that line wrapping is ugly...

2003-09-16, 00:24	#4
outlnder Aug 2002 13E₁₆ 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.