NFS results and reservations
 

NFS methods allow the full factorization of a given composite. GNFS is much slower but is suitable for numbers of general form. SNFS is faster but is restricted to numbers of special form, e.g. sextic a*b[sup]6[/sup]+c*d[sup]6[/sup] or quintic a*b[sup]5[/sup]+c*d[sup]5[/sup] for Leyland numbers. More information about the polynomial selection is available there:
[url]http://www.mersennewiki.org/index.php/SNFS_Polynomial_Selection[/url]

The measure of the difficulty is the decimal length of the polynomial value. GNFS difficulty is usually the same as the composite length, while SNFS difficulty may be much larger. Difficulty up to 165 for GNFS and up to 240 for SNFS is suitable for a single machine. Sextic SNFS polynomial is usually preferable over quintic for difficulty > 220.

GNFS on a composite cofactor become faster than SNFS on a full number if GNFS difficulty is less than ~70% of SNFS difficulty.

Some ECM pre-factoring is necessary to remove small factors before running an NFS job, stopping when the expected factor size is about 31% of GNFS difficulty or 22% of SNFS difficulty. E.g., t55 is enough for 175-digit GNFS or 250-digit SNFS job.

There's an introduction to NFS programs written by Jeff Gilchrist: [url]http://gilchrist.ca/jeff/factoring/nfs_beginners_guide.html[/url]
YAFU utility can automatically handle SNFS polynomials for Leyland numbers: [url]http://sourceforge.net/projects/yafu/[/url]

You may either take a provided [url=http://www.mersenneforum.org/showthread.php?t=19352]SNFS[/url] / [url=http://www.mersenneforum.org/showthread.php?t=19353]GNFS[/url] target, or pick up a certain number from [url=http://xyyxf.at.tut.by/cmplist.txt]the list[/url] and perform manual ECM pre-factoring, taking into account the status info: [url]http://www.primefan.ru/xyyxf/status.html#0[/url]

Note that your factorization may fit a Top-20: [url]http://www.primefan.ru/xyyxf/records.html#0[/url]
In such a case please submit the required information (e.g. wall-clock running time).

NFS Results
 

ryanp seems to have factored [url=http://www.factordb.com/index.php?query=111%5E100%2B100%5E111]C197_111_100[/url].

ryanp has [url=http://factordb.com/index.php?query=110%5E113%2B113%5E110]fully factored the remaining cofactor of 113_110 via GNFS[/url].

C222_115_98 fully factored
 

A [URL="http://factordb.com/index.php?query=115%5E98%2B98%5E115"]p57 and p58[/URL] were found.

More ryanp results
 

99^116+116^99 by SNFS: [URL="http://factordb.com/index.php?id=1000000000044718140"][COLOR=#0066cc]http://factordb.com/index.php?id=1000000000044718140[/COLOR][/URL]

and 93^116+116^93 (SNFS) [URL="http://factordb.com/index.php?id=1000000000044712140"][COLOR=#0066cc]http://factordb.com/index.php?id=1000000000044712140[/COLOR][/URL]


Ryan reports that he has temporarily lost some computing power and is therefore "holding off at the moment". He will let us know when he's back factoring at full capacity.

Reserving C168_130_71 and C168_134_94 for NFS@Home as GNFS tasks, due to the upcoming BOINC challenge.
At that difficulty, 15e would be more efficient than 14e, but if the 14e queue depletes faster than the 15e queue, they may go through 14e, I guess.

Ryan has factored another [url]http://factordb.com/index.php?id=1000000000044716140[/url], via SNFS presumably.

113_78 Factored by SNFS
 

Ryan nailed another one. See [url]http://factordb.com/index.php?id=1000000000044697137[/url].

Confirmed that the previous factor was also SNFS.

2 More Results (SNFS)
 

Ryan reports the following:

101^113+113^101 -- [url]http://factordb.com/index.php?id=1000000000044720137[/url]
110^111+111^110 -- [url]http://factordb.com/index.php?id=1000000000044729135[/url]

These two will be added as late as the next update :)

[url]http://xyyxf.at.tut.by/results.html#0[/url]

Reserving C184_120_61
 

For SNFS. Thanks.

C160_133_60
 

Factors by GNFS, 7 weeks.

[code]
prp97 = 7082538396843516920199135230943438701049415241033476093557924014144372365566104458277792491883807
prp63 = 478018421476975832068057613522486521348371199183670859015988429
[/code]

C160_133_47
 

GNFS, 14 weeks

[code]
prp72 = 120048784209828540645280430753347306215307102359630838208442444100533139
prp89 = 14965850008106312445199820343633470771296879449620427859991330582950011515609194211819927
[/code]

C163_148_50
 

Reserving C163_148_50 for SNFS (with a bit of preprocessing ECM).

Thanks.

C196_112_8​9
 

According to factordb, this number was [URL="http://factordb.com/index.php?query=112%5E89%2B89%5E112"]fully factored[/URL] on 9 June. Presumably by Ryan using SNFS, but this is unverified. He must be busy IRL, as he hasn't answered e-mail.

Hope that was him :-)

[url]http://xyyxf.at.tut.by/results.html#0[/url]

C184_120_61 Factored (SNFS)
 

[code]
prp86=64820580267076218837413083123642196952475956337959006868693801579029662809193550215173
prp99=150322207983195825884373262426186186539234540818588731324810662385895186905457233888336722789525031
[/code]

Results reported to factordb.

Ryan is reserving C159_127_81 for factoring by NFS.

C175_129_50 reservation
 

Ryan is taking C175_129_50 for factoring with SNFS.

127_81 factored by SNFS
 

Ryan's results [url=http://www.factordb.com/index.php?query=127%5E81%2B81%5E127]here[/url].

C175_129_50 factored by SNFS
 

Ryan also factored C175_129_50 by SNFS. Results [url=http://factordb.com/index.php?id=1000000000044669153]here[/url].

Sorry for the lack of reservation - it took him < 1 day start to finish.

C183_115_96 factors
 

Ryan found another - C183_115_96.

Results are [URL="http://factordb.com/index.php?id=1000000000044715139"]here[/URL].

Ryan is working a few numbers

C168_113_88
C192_115_79
C210_115_83
C221_113_100
C161_149_41

C192_115_79 Factored
 

Ryan found it via SNFS. [URL]http://factordb.com/index.php?id=1000000000044698139[/URL]

p94*p99, a nice split.

Ryan nailed another one, C210_115_83 by SNFS. See

[url]http://factordb.com/index.php?id=1000000000044702139[/url]

C175_126_55
 

I would like to reserve C175_126_55 for SNFS. Results expected in early October.

Thanks.

I noticed that there's a neglected very easy SNFS number still sitting in the composite file. (145_80, diff. 176)

I'll do it overnight, unless someone has done it actually.

EDIT: done. p82 * p89. In FactorDB.

[QUOTE=Batalov;382864]I noticed that there's a neglected very easy SNFS number still sitting in the composite file. (145_80, diff. 176)

I'll do it overnight, unless someone has done it actually.

EDIT: done. p82 * p89. In FactorDB.[/QUOTE]

:shock:

According to my test sieving, that job would take me 4-5 weeks on my unremarkable i7. What kind of rig do you have? What poly did you use?

Nice job.

With the x[SUP]4[/SUP] - x[SUP]3[/SUP] + x[SUP]2[/SUP] - x +1 poly, it is a very easy job: 100-core hours (overnight with 12 cores).
[CODE]n: 223338679141350214286564392611794940148102227633364681044488540131751666322287884308052364320927680226370657685408223566750766331340932329490285272461466096761672036508901
c4: 1
c3: -1
c2: 1
c1: -1
c0: 1
Y1: 250246473680347348787521
Y0: -101412048018258352119736256430080000000000000
type: snfs
skew: 1[/CODE]
There are no more missed reducibles in the list; I've played with some possible, hidden Aurifeuillians and haven't found any. There are some powers in the list like 128_125, many more 128s, a 64, a 32, some 121s and 125s, but they don't help. All reducibles (by 3, by 5, by 7) were done ages ago. I was surprised to see this one.

C168_113_88
 

Ryan got another. C168_113_88 is factored by SNFS:
[url]http://factordb.com/index.php?id=1000000000044707137[/url]

C221_113_100
 

Ryan Propper got another one by SNFS - C221_113_100

[URL="http://factordb.com/index.php?id=1000000000044719137"][COLOR=#0066cc]http://factordb.com/index.php?id=1000000000044719137[/COLOR][/URL]

Another Ryan reservation
 

C211_132_47
C197_119_67
C188_114_89
C191_111_101

C197_115_104

Thanks.

[QUOTE=swellman;383080]C197_115_104[/QUOTE]But that's the number reserved by you. Move it to Ryan?

[QUOTE=XYYXF;383083]But that's the number reserved by you. Move it to Ryan?[/QUOTE]

Yes, you can move it to Ryan. I've run over 17k curves on it @B1=110M to no avail. It will finish full t55 tonight - if it does hit I'll alert Ryan but I think he's safe.

Sorry for the confusion.

How much wall-clock time took that C221?

Ryan says according to his logs it took 28 hours.

[QUOTE=swellman;381825]Ryan's results [url=http://www.factordb.com/index.php?query=127%5E81%2B81%5E127]here[/url].[/QUOTE]C159_127_81 looks like GNFS job, not SNFS (difficulty 243).

[QUOTE=XYYXF;383114]C159_127_81 looks like GNFS job, not SNFS (difficulty 243).[/QUOTE]

No he says it was specifically a SNFS job. Ryan used the "snfspoly
helper program" in the xyyxf yahoo group to generate the poly for this number. He even overseived the job the first time and then had to rerun LA with less relations. Which is kind of scary...

Updated: [url]http://xyyxf.at.tut.by/status.html[/url]

:)

Updated: [url]http://xyyxf.at.tut.by/results.html#0[/url]

[QUOTE=swellman;383118]No he says it was specifically a SNFS job. Ryan used the "snfspoly
helper program" in the xyyxf yahoo group to generate the poly for this number. He even overseived the job the first time and then had to rerun LA with less relations. Which is kind of scary...[/QUOTE]

Any idea what parameters to feed that program? I just compiled it and am looking at the source code, but I've no idea.

One feeds snfspoly the degree of the polynomial on the command line (optionaly, by default 5, I usually use 6), then one enters Cnnn_X_Y interactively.

For instance:
[code]$ ~/snfspoly/snfspoly
C159_127_81
Original C159_127_81 contains 243 digits
Y^X=3^508
X^Y=127^81
Y^X=3^508

Poly file:
********
n: <copy from file>
name: C159_127_81
#X^Y=(127^1)*(127^16)^5
#Y^X=(3^3)*(3^101)^5
deg: 5
c5: 27
c0: 127
Y1: 4579937329576774398276408998492161
Y0: -1546132562196033993109383389296863818106322566003
type: snfs
skew: <vary from 1 to 10 and check secs/rel number>
********
1.528302 ratio : C159_127_81 with 243 digits[/code]

[code]$ ~/snfspoly/snfspoly 6
C159_127_81
Original C159_127_81 contains 243 digits
Y^X=3^508
X^Y=127^81
Y^X=3^508

Poly file:
********
n: <copy from file>
name: C159_127_81
#X^Y=(127^3)*(127^13)^6
#Y^X=(3^4)*(3^84)^6
deg: 6
c6: 81
c0: 2048383
Y1: 2235879388560037062539773567
Y0: -11972515182562019788602740026717047105681
type: snfs
skew: <vary from 1 to 10 and check secs/rel number>
********
1.528302 ratio : C159_127_81 with 243 digits[/code]

Nifty! Thanks!

I had a request for a Windows version of snfspoly, so I'm uploading it here. It's 64-bit (built in MinGW-64) compiled with GMP 6.0.0.

[QUOTE=wombatman;383216]I had a request for a Windows version of snfspoly, so I'm uploading it here. It's 64-bit (built in MinGW-64) compiled with GMP 6.0.0.[/QUOTE]

Needs the gmp library dll, or compile gmp statically?

Not sure if I did it right (but it compiled and runs fine), but try this one.

C161_149_41
 

It has been [URL="http://factordb.com/index.php?id=1000000000044660173"]factored[/URL] by GNFS, courtesy of Ryan P.

[code]
p79: 5254652404574501306652832473719273172694314626914965256618619243605730989842289
p82: 7245027671189122787015008209172851099700830390545655251779716558827050360389135031
[/code]

[QUOTE=wombatman;383240]Not sure if I did it right (but it compiled and runs fine), but try this one.[/QUOTE]

:tu:

[QUOTE=swellman;383249]It has been [URL="http://factordb.com/index.php?id=1000000000044660173"]factored[/URL] by GNFS[/QUOTE]Wall-clock time? :)

[QUOTE=XYYXF;383564]Wall-clock time? :)[/QUOTE]

The email announcing he was starting to look at the C161 and the email with the factors found are separated by 47 hours. Slow for Ryan but that includes a poly search.

Call it two days.

Jesus. What kind of firepower is he working with? It would take me a few weeks at best for a C161 by GNFS.

I don't know but it is [url=http://www.mersenneforum.org/showpost.php?p=377767&postcount=17]considerable[/url].

[QUOTE=wombatman;383571]Jesus. What kind of firepower is he working with? It would take me a few weeks at best for a C161 by GNFS.[/QUOTE]

Hints I've picked up around the forum indicate something like a handful of academic computer labs, perhaps 100 machines. I think the more interesting curiosity concerns the scripts he has created to harness all that power!

He's tackled GNFS190+ on his own...

Man, that must be nice...I'm rocking a solid 3 computer setup--2 desktops (one pieced together from old parts) and a laptop! WOOOO! :smile:

C211_132_47 factored
 

Ryan factored another, this time by SNFS.

[url]http://factordb.com/index.php?id=1000000000044666156[/url]

C197_119_67 factored (SNFS)
 

Another found by Ryan, this time it took three days. p73*p124


[url]http://factordb.com/index.php?id=1000000000044686143[/url]

C162_134_71 factored
 

[URL]http://factordb.com/index.php?id=1100000000032298190[/URL]

p69*p94

I got this with GNFS in about 7 weeks of noncontinuous runtime.

C162_131_88 (GNFS)
 

8 weeks

[url]http://www.factordb.com/index.php?id=1100000000639298928[/url]

[code]
prp77 = 28887625366182981990573317865436832821531637749406045585618871037303719459083
prp86 = 31311184739975754982559405371019664358764342048608451965565238531041064582692047501909
[/code]

Here we are: [url]http://xyyxf.at.tut.by/results.html#0[/url]

114^89+89^114 fully factored
 

Ryan accomplished it by SNFS. Results are found at

[url]http://factordb.com/index.php?id=1000000000044708138[/url]

C175_126_55 factored
 

[url]http://factordb.com/index.php?id=1000000000044674150[/url]

p64*p112

Factored using SNFS (4 weeks).

C197_115_104 Factored
 

Ryan nailed another one by SNFS.

[url]http://factordb.com/index.php?id=1000000000044723139[/url]

Ryan Reservation
 

All by SNFS

C177_126_61
C190_120_67
C160_119_73
C169_138_47
C176_127_63

And Ryan already finished 126_61!

[url]http://factordb.com/index.php?id=1000000000044680150[/url]

Thanks.

Ryan factored 120_67
 

[url]http://factordb.com/index.php?id=1000000000044686144[/url]

P85*P105

Ryan factorization of C160_119_73
 

Also by SNFS. P54*P107

[url]http://factordb.com/index.php?id=1000000000044692143[/url]

C175_123_73 factored by SNFS
 

Factored by the NFS@Home, details are [URL="http://www.mersenneforum.org/showpost.php?p=386379&postcount=1630"]here[/URL].

C185_125_53 (SNFS)
 

Reserving C185_125_53 for SNFS. Should be factored by mid January.

Thanks.

There are 3 polys for it: [url]http://mersenneforum.org/showthread.php?t=19352[/url]

Which one did you take? :-)

[QUOTE=XYYXF;391063]There are 3 polys for it: [url]http://mersenneforum.org/showthread.php?t=19352[/url]

Which one did you take? :-)[/QUOTE]

Quintic (difficulty 216): (53^25)^5 + 625*(5^31)^5 = 10941755890309490995358069318266 * C185

It should finish by late next week.

C191_111_101 factored by SNFS
 

Ryan factored this composite in approximately 30 hours.

[code]
prp80 factor:
13064010457564812414809614954538949379779118936205595590340753333117145375704311

prp112 factor:
4696921666891217524559822022117808836501821800945939947147358909847327620378952929835719285271171508437515297327

[/code]

C163_148_50 factored (SNFS)
 

[code]
p69=239102935769593138043447185027994610471963415568392873284244864973921

p95=33905859348467028584287255086642845840073598363470179613214271566223333735650253824603982131457[/code]

(repost) 123^71+71^123 factored
 

[code]
Mon Jan 5 12:31:00 2015 prp95 factor: 39498752734489753640606804099420441711111818064254367734291658571564113545613506752975967738933
Mon Jan 5 12:31:00 2015 prp126 factor: 433404930066465544464380820740481161819446165283251704628991926549573405714251507232025681505727209612829234418336257551027983
[/code]

Log at [url]http://pastebin.com/NqVyqEEx[/url]

129^58+58^129 done
 

[code]
Wed Jan 7 15:03:20 2015 prp60 factor: 946130503006880858461265763819139579348511562271560842276269
Wed Jan 7 15:03:20 2015 prp143 factor: 43026707346855415440117787296935125633951150680004091249139978911676313884204791278928001761454869163345731964093014837943018004160134211242153
[/code]

NFS@home sieved; 50 hours for 9.4M matrix of weight 1006009712 on four threads of i7/4770K

C169_138_47 Factored (SNFS)
 

Ryan factored another

[code]
prp69 factor:
668618062003586667557863170796505963556898654819502232801140119818809
prp100 factor:
9181697938923608941825240988112796344430180212715865638060236324583338888470549876700111484644531101
[/code]

[QUOTE=swellman;390942]Reserving C185_125_53 for SNFS. Should be factored by mid January.

Thanks.[/QUOTE]

[code]
p80=58707778038162323062145039886164681487902625220828337623661497335628973865158521

p105=532967878211077634004602529587841136191525360987694054859582314761989447195693751648664919095479881938213
[/code]

The pages are updated, please check: [url]http://xyyxf.at.tut.by/results.html#0[/url]

C176_127_63 factored (SNFS)
 

[code]
prp80 factor: 76469951543970116186970789663991981548758097184142072060572847850659844093100729
prp96 factor: 149486439662355245619419376924635884377938730293644593808470901192273827386679456228793950454363
[/code]

C171_111_107 factored
 

Ryan got another one using SNFS

[code]
prp69: 321691477600410878975266657260840766238264466541483668567219248893723
prp102: 883391217235268796684060457195562761816709303301511707609280378514557548640447010023513281845554228651
[/code]

C198_113_105 Fully factored
 

Factored by Ryan using SNFS
[code]
prp95=30579713868843130922376802571679579603798827862954272732953102997438317875881872680886264263737
prp104=27151358698096457288178129530819453088147528794968500725477161693011614960505045369148326295414176287873
[/code]

Please reserve C175_118_87 and C164_133_53 for Ryan.

Thanks.

C165_134_120 done
 

[code]
Thu Jan 29 22:00:49 2015 prp66 factor: 678695271492416308463140856340124524236269302537468243607698233153
Thu Jan 29 22:00:49 2015 prp99 factor: 676943041070359955358770894680544804069579305572092726364132773451378892151787361432118976453454337
[/code]

22 hours on i7/4770 -t4 for 6.4M matrix

C175_118_87 factored
 

Ryan has fully factored this number using SNFS.

[code]
prp71 factor: 11506460527447779180291864810319418170985076729937819257789302885989093
prp105 factor: 209812548218779873490830821649826523407854085127385847980551888435064018472428190182198550246380059293893
[/code]

C223_113_112 Factored
 

NFS@Home (SNFS)

[code]
prp63 factor: 259658816888575649802364504342298325136540174409150990503369367
prp71 factor: 11188521920618318874883608032543130205629249885943692412562942988595487
prp91 factor: 1564623699533884537827608582007255523107226027576742546555545462115829022694350139433043319
[/code]

C164_133_53 Factored
 

Ryan factored this with SNFS.

[code]
prp64= 1792665021985421057219160908693268114800243411800199889846838559
prp101= 50884560175258852148075640051109028877168200541264414149229476587907302306234848659086921077046137659
[/code]

Thanks for these NFS efforts :-)

Hope I listed them correctly there:
[url]http://www.primefan.ru/xyyxf/results.html#0[/url]

Please reserve the following for Ryan:

C226_115_97
C177_115_99
C164_133_55

Thanks.

Done. Note a C170 GNFS record :)

C226_115_97 Factored
 

Ryan factored it in two days using SNFS.

[url=http://factordb.com/index.php?id=1000000000044716139]p107*p119[/url]

Finally a p100+! Excellent :)

C177_115_99 Factored
 

Ryan again, and with SNFS.

[code]
prp77 factor: 57482138743270224754001796870172321008426990774257569646368733836123244722087
prp100 factor: 5341387392899652002209255393703604238157000032618341547619619930884078373829044947201073623984558107
[/code]

C199_113_92 factored
 

Ryan, using SNFS

[url=http://factordb.com/index.php?id=1000000000044711137]p86*p114[/url]

С137 is needed to update the pages :)
[url]http://mersenneforum.org/showpost.php?p=394923[/url]

[B]C185_113_82[/B] was factored by NFS@home.
[QUOTE=VictordeHolland;395543][code]prp77 factor: 58789541719310794464028451002607656177871970917892687975610948256126119656061
prp108 factor: 374323217276353022223811948834396954110231084098624184434102662550773803838656988732904473217686359002099431[/code]matrix is 6753906 x 6754132 (3147.7 MB) with weight 816313694 (120.86/col)
30 hours on a 3770k[/QUOTE]

C164_133_55 factored
 

Ryan got another, using SNFS.

[url=http://factordb.com/index.php?id=1000000000044674157]p66*p98[/url]



Please reserve C204_115_88 and C188_115_93 for Ryan.

Reserving C196_122_59 for factoring by SNFS.

C204_115_88 Factored
 

Another composite fully factored by Ryan.

[url=http://factordb.com/index.php?id=1000000000044707139]p65*p139[/url]

C188_115_93 Factored
 

Ryan factored another.

[url=http://factordb.com/index.php?id=1000000000044712139]p61*p127[/url]

C197_115_87
 

Ryan factored another.

[url=http://factordb.com/index.php?id=1000000000044706139]p76*p121[/url]

Please reserve C211_119_94 for Ryan.

Thanks.