[QUOTE=Miszka;556705][M]M3349033[/M] has a 201.952 bit composite factor: [url=https://www.mersenne.ca/M3349033]6217575158069946300914632364196267867798278947818161061977999[/url]
This is my second largest double factor.[/QUOTE]Ryan Propper (who else?) just edged you:[quote][M]M3163[/M] has a 202.010-bit (61-digit) factor: [url=https://www.mersenne.ca/M3163]6470824914532640346907398417629153527732878857898305930284399[/url] (ECM,B1=850000000,B2=14601464077218)[/quote]

Except, that's not a composite factor.. :showoff:

My [url=https://www.mersenne.ca/json2bbcode.php]Results to BBcode[/url] tool now checks for and handles composite factors:

[quote][M]M16929421[/M] has a 167.263-bit (51-digit) [b]composite[/b] (P22+P29) factor: [url=https://www.mersenne.ca/M16929421]224407487493587669391081856081164702441247338964631[/url] (P-1,B1=289000,B2=8238000,E=12)[/quote]

That would have been second-biggest P-1 factor if prime...

:cry:

Woah I think I finally found one worth of this thread!!!

[CODE][M]102038449[/M] is divisible by 9888494385519120122543174973655965293191066143473
[/CODE]

49 digits and 162.758 bits!!!

Unfortunately, it is composite, the smaller of which is less than 80 bits:
[CODE]797556068573591374225729
12398494319282704934063537[/CODE]

But I'm happy about it! The hunt continues...

Edit: I'm gonna run PRP-CF on it for fun, fingers crossed!

[QUOTE=Runtime Error;557264][M]102038449[/M] is divisible by 9888494385519120122543174973655965293191066143473[/QUOTE]Just curious, is that actual output from some factoring program, or did you format it that way? You appear to have run the P-1 with Prime95 which I thought would have output the usual [c]M102038449 has a factor: 9888...[/c] style?
Just wondering if I need to update my [url=https://www.mersenne.ca/json2bbcode.php]results bbencoder[/url] for that format if it's standard output from some program.

[QUOTE=James Heinrich;557279]Just curious, is that actual output from some factoring program, or did you format it that way? You appear to have run the P-1 with Prime95 which I thought would have output the usual [c]M102038449 has a factor: 9888...[/c] style?
Just wondering if I need to update my [url=https://www.mersenne.ca/json2bbcode.php]results bbencoder[/url] for that format if it's standard output from some program.[/QUOTE]

I formatted it to make it more elegant for human eyes. The output that I received is below. No need to update!!

[QUOTE]{"status":"F", "exponent":102038449, "worktype":"P-1", "factors":["9888494385519120122543174973655965293191066143473"], "b1":1000000, "b2":36000000, "brent-suyama":12, "fft-length":5898240, "security-code":"XYZXYZXYZ", "program":{"name":"Prime95", "version":"30.3", "build":6, "port":8}, "timestamp":"2020-09-17 12:17:30", "user":"XYZXYZXYZ"}[/QUOTE]

[QUOTE=Runtime Error;557290]I formatted it to make it more elegant for human eyes. The output that I received is below. No need to update!![/QUOTE]Oh, ok. That's what my results->bbencoder is for, just copy-paste in the JSON result line and you get this: :smile:[quote][M]M102038449[/M] has a 162.758-bit (49-digit) [b]composite[/b] (P24+P26) factor: [url=https://www.mersenne.ca/M102038449]9888494385519120122543174973655965293191066143473[/url] (P-1,B1=1000000,B2=36000000,E=12)[/quote]

[QUOTE=James Heinrich;557291]Oh, ok. That's what my results->bbencoder is for, just copy-paste in the JSON result line and you get this: :smile:[/QUOTE]

Ohhhh, wow TIL, thanks. I'll use bbencoder next time I find a good sized factor, which will hopefully be soon!

P-1 found a factor in stage #2, B1=722000, B2=19514000.
UID: Jwb52z/Clay, M100242643 has a factor: 2508386228544075871170604217209 (P-1, B1=722000, B2=19514000)

100.985 bits.

This is a big one for me.

It barely misses your personal Top 10: [URL="http://www.mersenne.ca/pm1user/789"]http://www.mersenne.ca/pm1user/789[/URL]

Even a blind (anonymous) squirrel finds a nut (factor) once in a while.
[M]54277[/M] has a factor of 2679778495314900465084978098198220983
37 digits 121 bits

[QUOTE=Uncwilly;557844][M]M54277[/M] has a 121.012-bit (37-digit) factor: [url=https://www.mersenne.ca/M54277]2679778495314900465084978098198220983[/url] (ECM,B1=3000000,B2=300000000)[/QUOTE]Yeah, I saw that yesterday and meant to comment, if only for the considerable number of P-1 efforts thrown at it.

TIL my largest factor is not even in the top 300.


[url]https://www.mersenne.ca/exponent/99797147[/url]


(32 digits, 105 bits)


[url]https://www.mersenne.ca/pm1user/1[/url]


(need 27 digits, 121 bits to get in top 300).

[QUOTE=phillipsjk;557853]TIL my largest factor is not even in the top 300.[/QUOTE]It's hard to get into the top list. I've been doing P-1 factoring for many years, I've found 2000+ factors, and only 3 of them are in the top-300 (none in the top-100). But it's mostly luck, so keep at it! :smile:

[QUOTE=James Heinrich;557856]It's hard to get into the top list. I've been doing P-1 factoring for many years, I've found 2000+ factors, and only 3 of them are in the top-300 (none in the top-100). But it's mostly luck, so keep at it! :smile:[/QUOTE]

It's clear you're not referring to the [URL="https://www.mersenne.org/report_top_500_p-1/"]Top P-1 Factoring Producers[/URL] list. I am #61 on that list. 117 factors in 5,569 tests. My largest factor, do date, is 39 digits. I didn't find it with P-1 though, but with ECM. I found that rather amazing.

[QUOTE=James Heinrich;557856]It's hard to get into the top list. I've been doing P-1 factoring for many years, I've found 2000+ factors, and only 3 of them are in the top-300 (none in the top-100). But it's mostly luck, so keep at it! :smile:[/QUOTE]
I've found 1400+ P-1 factors, and 9 of them are in the top-300. My biggest factor is in 23rd position.

P-1 found a factor in stage #1, B1=723000.
UID: Jwb52z/Clay, M100271917 has a factor: 77514042504246954650663761 (P-1, B1=723000)

86.003 bits.

2020-09-29 00:19 M235871 has a factor: 1354753690999656789045256961
2020-09-29 02:32 M339331 has a factor: 167369080256159138493834809
2020-09-29 06:29 M289789 has a factor: 75593232163993815783204345943
2020-09-29 07:45 M1871603 has a factor: 470279274234060910537


Individually they are nothing special, but 4 factors in 8 hours is really lucky. Normally I get 1 per day if things go well.

[M]M44053[/M] has a 119.154 bit factor: [url=https://www.mersenne.ca/M44053]739364366231468476552737013655785457[/url]

Notable in that it's the first ECM factor [url=https://www.mersenne.ca/userfactors/ecm/1311]I've found[/url] in 8 years (mostly for lack of trying).

Also an excellent segue to introduce the reworking of the Top Factors section of my site:
[url]https://www.mersenne.ca/userfactors[/url]
This replaces the Top P-1 Factors section but now adds ECM factors as well.

[QUOTE=James Heinrich;558281]Also an excellent segue to introduce the reworking of the Top Factors section of my site:
[url]https://www.mersenne.ca/userfactors[/url]
This replaces the Top P-1 Factors section but now adds ECM factors as well.[/QUOTE]

Were all the factors [URL="https://www.mersenne.ca/userfactors/ecm/1"]here[/URL] actually found by ECM?

[QUOTE=mathwiz;558284]Were all the factors [URL="https://www.mersenne.ca/userfactors/ecm/1"]here[/URL] actually found by ECM?[/QUOTE]Short answer: maybe. :smile:

Longer answer: PrimeNet thinks they were. Many of them certainly were. Unfortunately, back in the old days (2010 and older, perhaps more recently) PrimeNet didn't keep nearly as much data as it should about submissions -- in the early days PrimeNet would just "guess" on how a factor was found based on the size of the factor (if <xx-bit then TF, elseif <yy-bit then P-1, else ECM) so many older factors are incorrectly credited to ECM when they were actually found by P-1 or even TF. In generating the lists on mersenne.ca I have already filtered out the F-ECM results where the factor is smaller than the PrimeNet-default TF level. I'm fairly certain that all these are false-ECM results, but I'm also fairly certain that there are some false-ECM results still in there. The data has long since been lost (it was never recorded) so it's not easy to know for certain. Certainly small ones should likely be found by TF, very large ones by ECM, smooth ones by P-1, etc, but there's always a boundary area between the methods where a factor could conceivably be found by several methods.
But recent results (last... 5? years) should (nearly) all be accurate in terms of the correct factoring method, date of discovery, etc.

5 or 6 of the first 10 are (S)NFS factors. They made big news at their times (see 1061, the most recent, it was discussed on this forum and acclaimed a lot when it came. When sieving was started (it was announced), people here were betting on how large the factors will be, or even on the fact that it will be a 2-way or 3-way split (in fact, I think I was the only one betting on 3-way split, for fun, just to be "different" haha, even if all the odds were against :razz:). Maybe the others 3 or 4 are NFS, too. But PrimeNet doesn't record NFS stuff, so it recorded the factors like ECM. Maybe a mention is in order. The ECM [U][B]all times[/B][/U] records (for all types of numbers) are somewhere at 83 digits (if my memory serves right) and the first positions in tops are NOT mersenne numbers, so, for sure, those factors in top of your list aren't ECM.

[QUOTE=LaurV;558299]...so, for sure, those factors in top of your list aren't ECM.[/QUOTE]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=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.

[QUOTE=James Heinrich;558559]Unfortuantely (sic!) 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.[/QUOTE]
Scrolling (page changing) there doesn't work. Also: many old/small stuff was not found by P-1 because it was already found by TF to low limits :razz: (in spite of the fact that the middle of the table is not visible, the beginning and the end is, because the sorting by size/whatever, works well).

[QUOTE=LaurV;558575]Scrolling (page changing) there doesn't work.[/quote]Thanks, fixed now.
[QUOTE=LaurV;558575]Also: many old/small stuff was not found by P-1 because it was already found by TF to low limits[/QUOTE]No, this report only includes exponents where a NF-PM1 result was reported and then a factor was found to be in the range that the previous P-1 should have found but didn't.
For an example: [url=https://www.mersenne.ca/exponent/19998217]M19,998,217[/url] has a NF-PM1 reported on 2003-10-08, LL completed 2003-11-08, DC-LL completed 2007-12-03 (both a waste of time) and then 10 years after the failed P-1 a factor was found by TF on 2013-08-14.
When I generate data for this report I explicitly look for factors found [i]after[/i] the P-1 was done.

[QUOTE=James Heinrich;558596]data for this report I explicitly look for factors found [I]after[/I] the P-1 was done.[/QUOTE]


Are you the maintainer of mersenne.ca? I think some exponents in the list are actually results of glitches in data conversion, such as [M]50077721[/M]. It might be better to exclude those cases where P-1 date is unknown.


i.e., if a P-1 date is unknown, we treat it as done after the factor discovery. If a factor discovery date is unknown, we treat it as discovered during or before the P-1 run.

[QUOTE=Ensigm;558598]I think some exponents in the list are actually results of glitches in data conversion, such as [M]50077721[/M][/QUOTE]Thanks for highlighting a specific example. There was an illogic in part of my code that got the P-1 run and P-1 bounds disconnected. I have patched that and fixed it so it shouldn't happen any further. And that eliminates about 14k/16 exponents that were in the "missed by P-1" list.

From August 23rd. It may already be here somewhere. Anything shorter than 30 digits, I do not bother with...

[M]M100091029[/M] has a 101.349-bit (31-digit) factor: [URL="https://www.mersenne.ca/M100091029"]3228091182977790599237506837961[/URL] (P-1,B1=650000,B2=22000000)

ryan did it again


[code]
Ryan Propper
F-ECMFactor:

1270133764632902720778602923087552962031274925622407641153 / (ECM curve 1, B1=110000000, B2=900514153782, Sigma=11360005842630690070)
[/code]


as well as for 5231 and 5351 ( but slightly less impressive)

As we were talking about ECM records, I was looking to see if my memory still serves me right about those 83 digits, and found that there are some misconcordances between [URL="https://members.loria.fr/PZimmermann/records/top50.html"]this table[/URL] and [URL="https://www.mersenne.ca/userfactors/any/1/bits"]this table[/URL]. We have all their lines, but sometimes with different names (usually, anonymous, when the right names should be provided, even if they are not members of gimps, that would be fair for the discoverers), while they do NOT have all our lines, probably some of our records were not reported to them (like Ryan's M2671 factor). Somebody may report our records to them, so they become part of the "all times/all kinds" record history (not me, the discoverer should do it, but if they are not interested, maybe James?).

P-1 found a factor in stage #2, B1=723000, B2=19528000.
UID: Jwb52z/Clay, M100310531 has a factor: 54958127519802952206597652367 (P-1, B1=723000, B2=19528000),

95.472 bits.

Another big one. 42 digits, 138 bits

[CODE]M3667249 has a factor: 343439538302947378252521531857403032501081 (P-1, B1=30000000, B2=600000000, E=12)[/CODE]

Not my biggest, but still a top-40

[QUOTE=axn;559404]Another big one. 42 digits, 138 bits. Not my biggest, but still a top-40
[M]M3667249[/M] has a 137.979-bit (42-digit) factor: [url=https://www.mersenne.ca/M3667249]343439538302947378252521531857403032501081[/url] (P-1,B1=30000000,B2=600000000,E=12)[/QUOTE]Wow, impressive, congrats!

I was goofing with the GPU functions of GMP-ECM. The input cannot be larger than 2^1018. I was pulling test values out of the air when I came up with this:

[QUOTE]Composite cofactor ((((2^943-1)/41884514890068404473)/21698431)/62209711)/164511353 has 241 digits[/QUOTE]I am not sure how anyone would convert this to a single large number. Consider it a curiosity, amusement, or whatever. :grin:


[U]Edit[/U]: I thought about Yafu, so I ran this:

[QUOTE]yafu (2^^943-1)*41884514890068404473*21698431*62209711*164511353
[/QUOTE]And came up with this:

[QUOTE]691547141158611815988660322245152254658444810391024156084685520265851892528698195573824658968142416474365688635818459535379264569959609451020315792308103892844793652170248778874582185260236045114390228299259879386132422860579103312328382466032643920718110437396847181215829653041151849017588990719779703721487849925242727519103
[/QUOTE]

[QUOTE=storm5510;559447]I am not sure how anyone would convert this to a single large number. Consider it a curiosity, amusement, or whatever. :grin:[/QUOTE]PARI/GP, enter [c]print( ((((2^943-1)/41884514890068404473)/21698431)/62209711)/164511353 );[/c]
and you get your 241 digits:[code]7993740247389956264853174304168322255931238346246097321873539588852601041591321387921101681164706423023658390690691167622105779566348116865818161116278520751265794272168974387055181655888422451232542011347384356257680009348025432182336941183[/code]

And if you decide to factor that C241 with YAFU, you get:[code]***factors found***

P18 = 138325941036565103
P29 = 57644473457648767005697802783
P25 = 9280993516297855054039457
P171 = 108017532617736915133406584684682016398182243100347598313436462729073911856247557922662614974708675029796424611721425364738654561651249349759454300640753645387500306111631[/code]

[QUOTE=James Heinrich;559454]PARI/GP, enter [c]print( ((((2^943-1)/41884514890068404473)/21698431)/62209711)/164511353 );[/c]
and you get your 241 digits:[code]7993740247389956264853174304168322255931238346246097321873539588852601041591321387921101681164706423023658390690691167622105779566348116865818161116278520751265794272168974387055181655888422451232542011347384356257680009348025432182336941183[/code]And if you decide to factor that C241 with YAFU, you get:[code]***factors found***

P18 = 138325941036565103
P29 = 57644473457648767005697802783
P25 = 9280993516297855054039457
P171 = 108017532617736915133406584684682016398182243100347598313436462729073911856247557922662614974708675029796424611721425364738654561651249349759454300640753645387500306111631[/code][/QUOTE]

Yes, this is a composite. The largest single factor I found has 53 digits:

[QUOTE]20681466401231162257298375941479424220537996009370817
[/QUOTE] It only took a few seconds to run, but produced a 3,000+ line output file which I captured. It is attached below if anyone wants to look...

[QUOTE=LaurV;559180]there are some misconcordances between [URL="https://members.loria.fr/PZimmermann/records/top50.html"]this table[/URL] and [URL="https://www.mersenne.ca/userfactors/any/1/bits"]this table[/URL]. We have all their lines, but sometimes with different names (usually, anonymous, when the right names should be provided, even if they are not members of gimps, that would be fair for the discoverers), while they do NOT have all our lines, probably some of our records were not reported to them (like Ryan's [m]M2671[/m] factor). Somebody may report our records to them, so they become part of the "all times/all kinds" record history (not me, the discoverer should do it, but if they are not interested, maybe James?).[/QUOTE]I have sent Paul an email offering him some automated new-factor notification if he's interested.

@LaurV: since you brought it up, would you care to compile a list of the factors for which discover names are known but my site shows anonymous, please? Thanks! :smile:

If I can't keep my mouth shut... hihi.
Edit: Ok, I will look into it.
Edit 2: At first sight, [J. Bos/T. Kleinjung/A. Lenstra/P. Montgomery]'s factors, they factored many low mersennes by ECM and SNFS, but because none of them is member of Gimps, such factors were added to PrimeNet's DB like "anonymous". Or, in George's name (probably, he added the factor to the DB, there is no intention in "stealing" their factors) - the case for M1237.

Almost top 3
 

[M]M10017487[/M] has a 162.539-bit (49-digit) [b]composite[/b] (P23+P27) factor: [url=https://www.mersenne.ca/M10017487]8492545109166755533258311668299806208565163467423[/url] (P-1,B1=5000000,B2=150000000)

When I found this beauty in results.txt, I said: "Well, that will be composite...".

It was... :rant:

[QUOTE=Viliam Furik;559636][M]M10017487[/M] has a 162.539-bit (49-digit) [B]composite[/B] ([COLOR=DarkRed]P23+P27[/COLOR]) factor: [URL="https://www.mersenne.ca/M10017487"]8492545109166755533258311668299806208565163467423[/URL] (P-1,B1=5000000,B2=150000000)

When I found this beauty in results.txt, I said: "Well, that will be composite...".

It was... :rant:[/QUOTE]

I understand what a composite is. Would somebody like to elaborate on the "Pxx" references? :confused:

[QUOTE=storm5510;559663]I understand what a composite is. Would somebody like to elaborate on the "Pxx" references? :confused:[/QUOTE]

The composite factored into a 23 digit prime and a 27 digit prime.

[QUOTE=LaurV;559540]At first sight, [J. Bos/T. Kleinjung/A. Lenstra/P. Montgomery]'s factors, they factored many low mersennes by ECM and SNFS, but because none of them is member of Gimps, such factors were added to PrimeNet's DB like "anonymous". Or, in George's name (probably, he added the factor to the DB, there is no intention in "stealing" their factors) - the case for M1237.[/QUOTE]I have adjusted 3 factors to "Joppe Bos, Thorsten Kleinjung, Arjen Lenstra, Peter Montgomery", two were "anonymous", one was George.

There is an odd 4th case: [M]M1471[/M] which Zimmermann [URL="https://members.loria.fr/PZimmermann/records/top50.html"]credits[/URL] to Ryan Propper on 2017-Aug-31 but GIMPS data has [i]kkmrkkblmbrbk[/i] reporting it on 2017-09-03. It's possible that it was discovered outside GIMPS and reported (but not actually discovered) by [i]kkmrkkblmbrbk[/i] a few days later (edit: [url=https://mersenneforum.org/showthread.php?p=460881]this seems to support that[/url]), since I don't think Ryan Propper joined GIMPS until around 2019-Apr (at least that's when factors with his name on them start appearing).
So, should I change the credit for M1471 to Ryan? :unsure:

[QUOTE=James Heinrich;559672]There is an odd 4th case: [M]M1471[/M] which Zimmermann [URL="https://members.loria.fr/PZimmermann/records/top50.html"]credits[/URL] to Ryan Propper on 2017-Aug-31 but GIMPS data has [i]kkmrkkblmbrbk[/i] reporting it on 2017-09-03. It's possible that it was discovered outside GIMPS and reported (but not actually discovered) by [i]kkmrkkblmbrbk[/i] a few days later[/QUOTE]

Yep, that was me:

[CODE]GMP-ECM 6.4.4 [configured with GMP 6.0.0, --enable-asm-redc] [ECM]
Input number is
414112359191997701534253596492500106450300358197797860629666662626749053242608219494442402695651576837870340296832489287087736334825594271746068631644666774347474623919652707232075336460653035066984955186871523283455060667679907961096868238556949992989771660891724444656348335990462979243681517917537081864618887895837966964799536787373376827405632123493586648835674823827101723072520023440275366679460254103690151
(414 digits)
Using special division for factor of 2^1471-1
Using B1=850000000, B2=15892628251516, polynomial Dickson(30),
sigma=1149118327
dF=524288, k=5, d=5705700, d2=17, i0=132
Expected number of curves to find a factor of n digits:
35 40 45 50 55 60 65 70 75 80
15 47 168 661 2867 13623 69471 381778 2221086 1.4e+07
Step 1 took 10424603ms
Using 47 small primes for NTT
Estimated memory usage: 4389M
Initializing tables of differences for F took 13531ms
Computing roots of F took 265269ms
Building F from its roots took 107976ms
Computing 1/F took 43111ms
Initializing table of differences for G took 3177ms
Computing roots of G took 275418ms
Building G from its roots took 114795ms
Computing roots of G took 296465ms
Building G from its roots took 121469ms
Computing G * H took 20867ms
Reducing G * H mod F took 22248ms
Computing roots of G took 303952ms
Building G from its roots took 134736ms
Computing G * H took 21110ms
Reducing G * H mod F took 23203ms
Computing roots of G took 291818ms
Building G from its roots took 117351ms
Computing G * H took 20115ms
Reducing G * H mod F took 22810ms
Computing roots of G took 305851ms
Building G from its roots took 124813ms
Computing G * H took 19687ms
Reducing G * H mod F took 20117ms
Computing polyeval(F,G) took 207279ms
Computing product of all F(g_i) took 1019ms
Step 2 took 2901560ms
********** Factor found in step 2: 61491618977549042678155153540458255504752992030160252118535699943713
Found probable prime factor of 68 digits: 61491618977549042678155153540458255504752992030160252118535699943713
Probable prime cofactor 6734452045297304612995050904133968305694025489494814555211753778337449397088976789153790263210262363727443589087252640846370390818555151954319223922183531363828896443099275063889485014446803977469139684639880343219143574884603136545584618534007354180853969730250054739420717651286559832852943449096627017735640776807663419415624956377103688592327 has 346 digits[/CODE]

[QUOTE=ryanp;559680]Yep, that was me[/QUOTE]Thanks Ryan for the confirmation. I have adjusted the discovery credit/date and added B1/B2/Sigma details to the record.
If there are any factors of your discovery that are improperly credited (e.g. anonymous results presumably pre-dating your involvement with GIMPS) please let me know and I can adjust accordingly.

[QUOTE=James Heinrich;559672]but GIMPS data has [I]kkmrkkblmbrbk[/I] reporting it on 2017-09-03.[/QUOTE]
That's GP2 on the forum, and he posted public some time ago about adding this factor from Ryan to DB by himself. No foul play.
Edit: yep, that's the thread (I clicked on your link).

P-1 found a factor in stage #1, B1=723000.
UID: Jwb52z/Clay, M100395877 has a factor: 448253095742777764768529 (P-1, B1=723000),

78.569 bits.

[QUOTE][M]M54703547[/M] has a 109.134 bit factor: [URL="https://www.mersenne.ca/M54703547"]712247215779481049225767999609031[/URL][/QUOTE] After more than 1.5 months of hunting, finally got this, [URL="https://www.mersenne.ca/userfactors/pm1/54147/bits"]my first 100 bit P-1 factor[/URL] (or factor of any kind).

:tu: Nice hit! Wish you more in the future!

So close to being famous!

[CODE][M]M101006167[/M] has a 110.999-bit (34-digit) factor: [url=https://www.mersenne.ca/M101006167]2594169183397489325041810602506857[/url] (P-1,B1=698000,B2=19930000,E=12)[/CODE]

P-1 found a factor in stage #2, B1=725000, B2=19864000.
UID: Jwb52z/Clay, M100610971 has a factor: 2780765085517092630313224143 (P-1, B1=725000, B2=19864000),

91.168 bits.

P1 factor
[M]M30553459[/M] has a 75.522-bit (23-digit) factor: [url=https://www.mersenne.ca/M30553459]54238665985862635591711[/url] (P-1,B1=252000,B2=6412000,E=12)

[QUOTE=LaurV;560680]:tu: Nice hit! Wish you more in the future![/QUOTE]
Thanks, I did :lol:.
[CODE][M]M54819403[/M] has a 114.663-bit (35-digit) factor: [URL="https://www.mersenne.ca/M54819403"]32880114785402226619625740909343209[/URL] (P-1,B1=1815246,B2=45381154,E=12)[/CODE]

:groupwave:My notebooks are just spitting out factors these two days……expected rate should be about 3.8%, according to [URL]https://www.mersenne.ca/prob.php[/URL].

[QUOTE=Ensigm;561865]:groupwave:My notebooks are just spitting out factors these two days……expected rate should be about 3.8%, according to [URL]https://www.mersenne.ca/prob.php[/URL].[/QUOTE]

Lucky for you.... keep it up

[QUOTE=Ensigm;561865]:groupwave:My notebooks are just spitting out factors these two days……expected rate should be about 3.8%, according to [URL]https://www.mersenne.ca/prob.php[/URL].[/QUOTE]

I'm working on a range that should have close to a 3% (1/33) success rates.
The factor number and corresponding attempt numbers so far are:
1st: 28
2nd: 55
3rd: 263 (At this point 1/88)
4th: 321
5th: 334
6th: 343 (Better: 1/57)
7th: 482 (1/69)
.......520 (1/74 and counting)

[M]M30584327[/M] has a 81.881-bit (25-digit) factor: [url=https://www.mersenne.ca/M30584327]4452837427904455799823223[/url] (P-1,B1=435000,B2=13050000,E=12)


k= 3^2*7*479*71 437* 33 768 257


far above the B2, and close to the exponent.

[M]M573851[/M] has a 90.320-bit (28-digit) factor: [URL="https://www.mersenne.ca/M573851"]1544960751860681271073683793[/URL] (ECM,B1=250000,B2=25000000,Sigma=3382465195143985)

[QUOTE=storm5510;562740][M]M573851[/M] has a 90.320-bit (28-digit) factor: [URL="https://www.mersenne.ca/M573851"]1544960751860681271073683793[/URL] (ECM,B1=250000,B2=25000000,Sigma=3382465195143985)[/QUOTE]

Nice find! How many curves did you run? (Maybe I'm looking in the wrong places, but I don't see curve counts for the results line with factors found)

[QUOTE=masser;562745]Nice find! How many curves did you run? (Maybe I'm looking in the wrong places, but I don't see curve counts for the results line with factors found)[/QUOTE]According to the PrimeNet results, [i]storm5510[/i] ran 6 curves and then found this factor. 424 other curves had been run by other users prior to finding the factor.

[QUOTE=masser;562745]Nice find! How many curves did you run? (Maybe I'm looking in the wrong places, but I don't see curve counts for the results line with factors found)[/QUOTE]

The default automatic reservation from [I]PrimeNet[/I] is 7 curves for ECM.

My largest-ever find was 39 digits. As a general rule, I don't post anything now less then 30 digits, but it had been a while since I had posted anything at all, so I thought, why not...

:smile:

Another factor !
[M]M32109773[/M] has a 87.489-bit (27-digit) factor: [URL="https://www.mersenne.ca/M32109773"]217225910846909775855945167[/URL] (P-1,B1=500000,B2=15000000,E=12)


Nice and large!

3 in a row on my results page
 

[CODE]Manual testing 29209879 F 2020-11-13 00:45 0.0 Factor: 4531021175987334651209 / TF: 71-72 15.3960
Manual testing 29209853 F 2020-11-13 00:45 0.0 Factor: 1372528680708957106817 / TF: 70-71 1.7791
Manual testing 29209777 F 2020-11-13 00:45 0.0 Factor: 2937064028034979220513 / TF: 71-72 5.1553[/CODE]

OK I lied just a bit (not Donaldish).

The factors are reported in a row by misfit; but I still got 3 out of 8 attempts and 2 were consecutive

And another pair...truly consecutive assignments
 

[CODE]Sid & Andy Manual testing 44646643 F 2020-11-13 22:40 0.0 62.3632 Factor: 31281450177560922551089 / TF: 74-75*
Sid & Andy Manual testing 44646619 F 2020-11-13 22:40 0.0 52.8812 Factor: 28972011828164945454479 / TF: 74-75*[/CODE]

P-1 found a factor in stage #1, B1=729000.
UID: Jwb52z/Clay, M101146343 has a factor: 498059508840817429391615399 (P-1, B1=729000)

88.686 bit.

P-1 found a factor in stage #2, B1=500000, B2=15000000
M32120479 has a factor: 704279413979608134427969766927( P-1, , B1=500000, B2=15000000)


99.152 bits

I know, it is a composite but still
[M]M32148013[/M] has a 171.369-bit (52-digit) [B]composite[/B] (P26+P27) factor: [URL="https://www.mersenne.ca/M32148013"]3866049125437654294832342492322663453310186293606097[/URL] (P-1,B1=500000,B2=15000000,E=12)


3866049125437654294832342492322663453310186293606097=13036577178475811829280543 * 296554001292665871025982479

[QUOTE=firejuggler;563879]I know, it is a composite but still
[M]M32148013[/M] has a 171.369-bit (52-digit) [B]composite[/B] (P26+P27) factor: [URL="https://www.mersenne.ca/M32148013"]3866049125437654294832342492322663453310186293606097[/URL] (P-1,B1=500000,B2=15000000,E=12)


3866049125437654294832342492322663453310186293606097=13036577178475811829280543 * 296554001292665871025982479[/QUOTE]
Impressive! Really hope I can get a fat composite factor someday too. (If the probability of a factor within a set of P-1 bounds is independent of the presence of another factor, then that day could be only a few months away,)

[URL="https://www.mersenne.org/report_exponent/?exp_lo=14039173&full=1"]M14039173[/URL] has a factor: 4281610697981019482542271 (P-1, B1=550000, B2=550000, e=12, n=800K CUDAPm1 v0.22)

P-1 = 4 281610 697981 019482 542270 = 2 × 5 × 131 × 193 × 2243 × 20147 × 26693 × 14 039173

Another factor missed by late-2001 P-1 result.

[QUOTE=masser;564019][URL="https://www.mersenne.org/report_exponent/?exp_lo=14039173&full=1"]M14039173[/URL] has a factor: 4281610697981019482542271 (P-1, B1=550000, B2=550000, e=12, n=800K CUDAPm1 v0.22)

P-1 = 4 281610 697981 019482 542270 = 2 × 5 × 131 × 193 × 2243 × 20147 × 26693 × 14 039173

Another factor missed by late-2001 P-1 result.[/QUOTE]

I believe this was found by the Brent Suyama extension. The last factor of K is very high

[QUOTE=masser;564019]P-1 = 4 281610 697981 019482 542270 = 2 × 5 × 131 × 193 × 2243 × 20147 × 26693 × 14 039173[/QUOTE][QUOTE=petrw1;564026]I believe this was found by the Brent Suyama extension. The last factor of K is very high[/QUOTE]No, the last factor as written by [i]masser[/i] is the [url=https://www.mersenne.ca/exponent/14039173]exponent[/url], as expected.
Remembering that Mersenne factors occur in the form of 2 * exponent * k + 1, in this case:
4281610697981019482542271 = 2 * 14039173 * (5 × 131 × 193 × 2243 × 20147 × 26693) + 1
([i]masser[/i] expressed this with 1 removed from both sides)

The factor should have been found in stage1 of the original P-1 run in 2001, another victim of buggy P-1 implementation in early Prime95.

[QUOTE=James Heinrich;564028]No, the last factor as written .....[/QUOTE]
:redface:

[QUOTE=James Heinrich;564028]The factor should have been found in stage1 of the original P-1 run in 2001, another victim of buggy P-1 implementation in early Prime95.[/QUOTE]

Are there enough errors that its worth redoing all early P1s from a certain time frame? Wouldn't take nearly as long now

[QUOTE=petrw1;564054]Are there enough errors that its worth redoing all early P1s from a certain time frame? Wouldn't take nearly as long now[/QUOTE]Probably. A handful of us are already redoing badly-done P-1 in the 10M-20M range and [url=https://www.mersenne.ca/p1missed.php?min=10000000&max=19999999]found a bunch[/url]. I can't speak for anyone else but I'm working through all the poor-probability (mostly stage1-only) P-1 up to 20M, and finding a fair number of factors for relatively little effort. Some of these may have been missed-factors, others just because previous bounds were too low, I haven't investigated. Possibly at some point it would be worth compiling a list of exponents with no known factors that had a NF-PM1 reported during the probably time period (prior to 2003?) and having a go at them. A project for next year, perhaps.

68613220[B][U]8655568[/U][/B]5453458891018563364263564767270[B][U]3702073[/U][/B]263
Composite factor found for 43028351 with P-1.
Has two 7-digit palindromes within it:

The corresponding Prime Factors
8490[B][U]68086[/U][/B]19428164689743
[B][U]808[/U][/B]100339433284836173218656436641
The smaller has a 5-digit palindrome within it.
The middle 3 digits of which are the beginning of the larger factor.

[QUOTE=James Heinrich;564055]Probably. A handful of us are already redoing badly-done P-1 in the 10M-20M range and [URL="https://www.mersenne.ca/p1missed.php?min=10000000&max=19999999"]found a bunch[/URL]. I can't speak for anyone else but I'm working through all the poor-probability (mostly stage1-only) P-1 up to 20M...[/QUOTE]

I used to run some of these. I would take an entire list of 500 and save it to a file, and run them in order in smaller groups. I used [I]Prime95[/I], avoiding the extra step in getting AID's then moving them to something else. I never felt [I]Prime95's[/I] bounds were high enough, and I was never sure how many it would allow me reserve in each group without cutting my list off somewhere at the bottom. The most I ever tried was 50.

What I ran then were all between 7e6 and 8e6. I just generated another list. What I see now starts just below 37e5 and ascends rapidly, so some new ones have been added to the lower end.

[quote][M]M12469069[/M] has a 209.296-bit (64-digit) [b]composite[/b] (P30+P34) factor: [url=https://www.mersenne.ca/M12469069]1010407523290974831570787304355977539700408276934619634505308431[/url] (P-1,B1=635000,B2=27600000,E=12)[/quote]

But I can't take credit for that. It was actually found in 2001 by "chbarr2". However, for a short while in those early days, PrimeNet would accept composite factor results but only record the first/smallest prime factor. I discovered this by accident, so I went through all the result logs looking for where a composite factor was reported but not all prime component factors were recorded. I found about a dozen, and they have all been "rediscovered" and recorded now, and back-dated to their original date of discovery. Also note that in those early days, PrimeNet kept no record of factor discovery method, all factors were just lumped together with TF results.

George just found a biggy:
[M]100817777[/M] has a factor 7594873610247018123015770141312996569
37 digits 122.5 bits

Ken found a big one too:
[m]101273659[/m] has a factor 375324496211112358228921438201039041097
39 digits 128.1 bits

And George's wasn't even with Prime95 (but rather gpuowl).

P-1 found a factor in stage #1, B1=746000.
UID: Jwb52z/Clay, M101488399 has a factor: 318084054463279132879217 (P-1, B1=746000),

78.074 bits.

[QUOTE=Jwb52z;565517]P-1 found a factor in stage #1, B1=746000.
UID: Jwb52z/Clay, M101488399 has a factor: 318084054463279132879217 (P-1, B1=746000),

78.074 bits.[/QUOTE]

M318084054463279132879217 has a factor: 1908504326779674797275303

(and no, M1908504326779674797275303 has 0 factors in [2^1, 2^120-1]) :smile:

[QUOTE=petrw1;564026]I believe this was found by the Brent Suyama extension. The last factor of K is very high[/QUOTE]

M4281610697981019482542271 has a factor: 466661313194347275441247200833

M466661313194347275441247200833 has 0 factors in [2^1, 2^132-1]

:et_:

M197 has a factor: 26828803997912886929710867041891989490486893845712448833 (already known)
But M26828803997912886929710867041891989490486893845712448833 has a factor: 126363666830169697438938183767311270500193270013305634003431 (196.3313 bit)
:big grin:

Bruno Victal turned in a 128.456 bit (39 digit) factor for [B]M[M]8017[/M][/B]
466627910317083433103066106476038970159
All known prime factors for it now total 90 digits on a 2414 digit number.

Grrrr... please stop posting trivial factors of ridiculously huge mersenne numbers. It was fun for the first few, and took us by surprise, but they don't have any value.
If you are serious, beat this.
M(2618163402417 · 2[SUP]1290000[/SUP]-1) has a factor 2618163402417 · 2[SUP]1290001[/SUP]-1 (1290043 bits)
(the largest "trivial" known, since 2016)

Our largest P-1 factor ever: [C]34925362324925878138544818314286841[/C]

:mike:

Congrats! New [url=https://www.mersenne.ca/userfactors/pm1/5216/bits]record[/url]! :whee: