[QUOTE=James Heinrich;558337]If you want to provide me a sublist of factors from that list that cannot possibly be ECM, or perhaps some criteria that I could walk through the database and weed out the non-ECM ones (as I did with the below-TF-limit ones) I'd be happy to trim the database.[/QUOTE]

These were all done by NFS, per the [URL="https://homes.cerias.purdue.edu/~ssw/cun/oldp/index.html"]Cunningham tables site[/URL]:

1061
1129
991
1193
1151
863
823
1153
853
827
1019
857 (both factors)
1031
887
877
941
859
821
929

I think this is all of them, though there's a small chance that I could have missed a GNFS factorization of a slightly larger exponent.

[QUOTE=charybdis;558350]These were all done by NFS, per the [URL="https://homes.cerias.purdue.edu/~ssw/cun/oldp/index.html"]Cunningham tables site[/URL]:
I think this is all of them, though there's a small chance that I could have missed a GNFS factorization of a slightly larger exponent.[/QUOTE]Thanks, I have removed those from the data.

Ryan strikes again, [STRIKE]4[/STRIKE] [STRIKE]6[/STRIKE] 10 new factors for very small exponents within the space of [STRIKE]an hour[/STRIKE] a few hours:[quote][M]M4157[/M] has a 144.884-bit (44-digit) factor: [url=https://www.mersenne.ca/M4157]41161769340018076868666055145622172588108913[/url] (ECM,B1=110000000,B2=900514153782)
[M]M4259[/M] has a 138.475-bit (42-digit) factor: [url=https://www.mersenne.ca/M4259]484399053828087857927777245183883458323463[/url] (ECM,B1=110000000,B2=900514153782)
[M]M4297[/M] has a 136.147-bit (41-digit) factor: [url=https://www.mersenne.ca/M4297]96437429855240462114489441553704488059887[/url] (ECM,B1=110000000,B2=900514153782)
[M]M4327[/M] has a 128.869-bit (39-digit) factor: [url=https://www.mersenne.ca/M4327]621316165862254523582603721415095832031[/url] (ECM,B1=110000000,B2=900514153782)

[COLOR="SeaGreen"][M]M4349[/M] has a 135.127-bit (41-digit) factor: [url=https://www.mersenne.ca/M4349]47571370031120172757491816499652518228991[/url] (ECM,B1=110000000,B2=900514153782) ** now fully factored[/COLOR] :cool:
[M]M4027[/M] has a 159.856-bit (49-digit) factor: [url=https://www.mersenne.ca/M4027]1322603807888784213814883095222492416081030114751[/url] (ECM,B1=110000000,B2=900514153782) [COLOR="Indigo"]#123 largest[/COLOR]
[M]M4447[/M] has a 168.677-bit (51-digit) factor: [url=https://www.mersenne.ca/M4447]598222550497242756375642930033091976261520001812697[/url] (ECM,B1=110000000,B2=900514153782) [COLOR="Indigo"]#89 largest[/COLOR]
[M]M4273[/M] has a 173.500-bit (53-digit) factor: [url=https://www.mersenne.ca/M4273]16937472485366180815044482979818421310092932459932943[/url] (ECM,B1=110000000,B2=900514153782) [COLOR="Indigo"]#77 largest[/COLOR]
[M]M4339[/M] has a 184.369-bit (56-digit) factor: [url=https://www.mersenne.ca/M4339]31656104144718898310053878501271041700569421852927688143[/url] (ECM,B1=110000000,B2=900514153782) [COLOR="Indigo"]#56 largest[/COLOR]
[M]M4397[/M] has a 197.525-bit (60-digit) factor: [url=https://www.mersenne.ca/M4397]289041852087298746712043757073410343587428123771191294135823[/url] (ECM,B1=110000000,B2=900514153782) [COLOR="Indigo"]#27 largest[/COLOR][/quote]
edit: 5-10th ones a couple hours later. The 10th through 7th are now #27,56,77,89 on [url=https://www.mersenne.ca/userfactors/ecm/1]ECM biggest factors list[/url].
And [url=https://www.mersenne.ca/M4349]M4349[/url] is now [url=https://www.mersenneforum.org/showthread.php?p=558515#post558515]fully-factored[/url].

[QUOTE=charybdis;558350]These were all done by NFS
[/QUOTE]
Thanks, you saved me a lot of time to look for those.
Now the numbers in James' tables look more realistic (going down from 73 digits, and not from 150 :razz:). That's more like "ECM range". Some of the anon results may still be NFS, but I won't bother. One silly idea would be to parse the PrimeNet DB for "sigma" info, as per George, the info is recorded on the server (but not shown by the "beautified" print routine), and I think all newer ECM result (like in the last yy years) should have stored b1/b2/sigma if they are trully ECM results. The lower side is not really interesting, so, eliminating TF/P-1 possible factors or letting them in, won't hurt much either way.

[QUOTE=LaurV;558425]I think all newer ECM result (like in the last yy years) should have stored b1/b2/sigma if they are trully ECM results[/QUOTE]If the server parsed and stored sigma values from the effort then it would also have correctly recorded the factoring method. It's the "ancient" results that are questionable because they were basically parsed for "Mx has a factor: y", ignoring all other data, and then guessed if that factor was TF/P-1/ECM by the number of bits. So there's no corroborating data to confirm/deny ECM'ness of a factor.

[QUOTE=James Heinrich;558358]Thanks, I have removed those from the data.[/QUOTE]

[url]https://en.wikipedia.org/wiki/Integer_factorization_records#Numbers_of_a_special_form[/url] says: "All unfactored parts of the numbers 2[SUP]n[/SUP] − 1 with n between 1000 and 1200 were factored by a multiple-number-sieve approach in which much of the sieving step could be done simultaneously for multiple numbers, by a group including T. Kleinjung, J. Bos and A. K. Lenstra, starting in 2010."

So presumably we should exclude all [TEX]1000 <= n <= 1200[/TEX]?

[QUOTE=mathwiz;558520]So presumably we should exclude all [TEX]1000 <= n <= 1200[/TEX]?[/QUOTE]Whether we [i]should[/i] or not is beyond my knowing, I'll let others weigh in on that. The data involved:[code]| exponent | date_found | factorbits | factor |
+----------+---------------------+------------+---------------------------------------------------------------------------+
| 1013 | 2010-03-04 11:38:00 | 194.712 | 41120912566813018675472321435609728349473493582225344661873 |
| 1051 | 2010-08-08 10:46:00 | 207.069 | 215738012818441827932337543036174144558274385301234576636299249 |
| 1051 | 2013-08-09 11:24:00 | 227.5 | 305017906063256842921494808558019733856326299412534951989303214657199 |
| 1069 | 2013-08-02 15:16:00 | 231.687 | 5557036167944892502666285821951871600803581019193074182942021552512721 |
| 1087 | 2010-02-21 09:25:00 | 200.73 | 2664797814058212286560533454960446792210016180875809243599817 |
| 1163 | 2010-04-18 20:06:00 | 239.239 | 1042816042941845750042952206680089794415014668329850393031910483526456487 |
| 1181 | 2010-03-07 16:11:00 | 240.034 | 1808422353177349564546512035512530001279481259854248860454348989451026887 |
| 1187 | 2010-01-30 14:50:00 | 206.576 | 153327833285998453874202767942570343649971393640068204571694369 |[/code]

[QUOTE=mathwiz;558520][url]https://en.wikipedia.org/wiki/Integer_factorization_records#Numbers_of_a_special_form[/url] says: "All unfactored parts of the numbers 2[SUP]n[/SUP] − 1 with n between 1000 and 1200 were factored by a multiple-number-sieve approach in which much of the sieving step could be done simultaneously for multiple numbers, by a group including T. Kleinjung, J. Bos and A. K. Lenstra, starting in 2010."

So presumably we should exclude all [TEX]1000 <= n <= 1200[/TEX]?[/QUOTE]

The important word is "unfactored". Lots of these numbers had already been completely factored.

[QUOTE=James Heinrich;558523]Whether we [i]should[/i] or not is beyond my knowing, I'll let others weigh in on that. The data involved:[code]| exponent | date_found | factorbits | factor |
+----------+---------------------+------------+---------------------------------------------------------------------------+
| 1013 | 2010-03-04 11:38:00 | 194.712 | 41120912566813018675472321435609728349473493582225344661873 |
| 1051 | 2010-08-08 10:46:00 | 207.069 | 215738012818441827932337543036174144558274385301234576636299249 |
| 1051 | 2013-08-09 11:24:00 | 227.5 | 305017906063256842921494808558019733856326299412534951989303214657199 |
| 1069 | 2013-08-02 15:16:00 | 231.687 | 5557036167944892502666285821951871600803581019193074182942021552512721 |
| 1087 | 2010-02-21 09:25:00 | 200.73 | 2664797814058212286560533454960446792210016180875809243599817 |
| 1163 | 2010-04-18 20:06:00 | 239.239 | 1042816042941845750042952206680089794415014668329850393031910483526456487 |
| 1181 | 2010-03-07 16:11:00 | 240.034 | 1808422353177349564546512035512530001279481259854248860454348989451026887 |
| 1187 | 2010-01-30 14:50:00 | 206.576 | 153327833285998453874202767942570343649971393640068204571694369 |[/code][/QUOTE]

These are all genuine ECM factors. The ones from 2010 were found by Bos, Kleinjung et al, presumably in preparation for their SNFS factorizations. The other two, despite being listed as "ANONYMOUS", were in fact found by Ryan Propper.

[QUOTE=charybdis;558542]These are all genuine ECM factors. The ones from 2010 were found by Bos, Kleinjung et al, presumably in preparation for their SNFS factorizations. The other two, despite being listed as "ANONYMOUS", were in fact found by Ryan Propper.[/QUOTE]I don't know if any of Bos,Kleinjung,etal have Primenet usernames. I have updated M1051, M1069 to belong to Ryan.

[M]M13113773[/M] has a 70.491-bit (22-digit) factor: [URL="https://www.mersenne.ca/M13113773"]1659317092853794607729[/URL] (P-1,B1=1000000)


Interestingly, it should have been found by the earlier P-1

[QUOTE=firejuggler;558556]Interestingly, it should have been found by the earlier P-1[/QUOTE]Unfortuantely that's [url=https://www.mersenne.ca/p1missed.php?s=x&o=d&min=1000000&max=20000000]not at all uncommon[/url], due in no small part to a buggy P-1 implementation in early versions of Prime95.