[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).