Gratuitous factors thread - Page 4

themaster · 2008-10-01, 16:55

3125816322396491327908016847491033937128894943594234816697681006021363321771944734880578361789769904775235680462891977712703
= 23059 x 479274976453780697 (Curve 31) x 1009436544491716921163 (Curve 57) x
430197652347851365324169 (Curve 332) x 4556941504336643669106130417 x
142928131963475091552029641439 (SIQS)

quite a nice number of medium size factors

Batalov · 2008-10-01, 17:45

Bruce and Greg did this monstrosity -
http://mersenneforum.org/showpost.ph...&postcount=397

FactorEyes · 2008-10-01, 18:24

Quote:

Originally Posted by Batalov

Ok, just look for good ideas in what I just wrote, not for hidden insults. There are none! (At least none intended.)

Peace! --Serge

You did not pick on people who prefer quartics for SNFS jobs, so what you wrote is politically acceptable to me, and, being inoffensive to me, qualifies as legitimate free speech.

(Quintics and sextics are for whiners.)

Batalov · 2008-10-01, 18:57

Quartics? Now, paraphrasing The Graduate infamous hint: "Septics!"

__________

Mr. McGuire: I want to say one word to you. Just one word.
Benjamin: Yes, sir.
Mr. McGuire: Are you listening?
Benjamin: Yes, I am.
Mr. McGuire: Plastics.
Benjamin: Just how do you mean that, sir?

sean · 2008-10-02, 01:19

I have completed the factorization of 122!-1 by GNFS.

On 2000-02-11 David Miller found the factor 86931787124894025899613982958574289, leaving a C163. It took me 5 months with the Franke, Kleinjung, Bahr, et al. implementation of GNFS to complete the factorization of this number. This is my personal best for GNFS.

Code:

122!-1 139.1381.86931787124894025899613982958574289.5576508736105627548402879357332051369062018458499320479330647748552094650266337.P85

The config file was:

Code:

5917686603831398223364673435358357137280652296278084434087991373071815772650029267347702479825598785894524590493753852303353769977519673999810345326389649459944649
X5 1442880
X4 -16901347639083
X3 -8587858228985321843
X2 43202270329828664385398008
X1 -2656547829320952529053251445729
X0 -16135033462316010115027001103203281449
Y1 14865695238506713
Y0 -21017659422567500102090287663966
M 2341541861803943155263839678058508653484076369623228078635782207837116358579684473849075085246884117912305105122625113706595271848522729665000121875538951988596057
0 11000000 2.8 32 62
0 21000000 2.8 32 62

Sieving took 1.5 months on a variety of machines. The rest of the time was taken by the post-processing including the Lanczos reduction of a 8.8M matrix using my own Java port of the Franke lanczos code. The reduction was performed on a dual-core 1.8 MHz Opteron with 16GB of RAM.

The smallest n of the form n!-1 not yet completely factored is 131!-1. On the + side, 109!+1 still resists my best efforts with ECM. The smallest composite of these forms not yet factored is 144!+1 C163.

bsquared · 2008-10-03, 13:46

That's quite an effort sean, nice job!

If you remember, can you say anything about what parameters you used for polynomial selection, assuming you used pol51*?

I'm working on a C145 right now, and while the size of the number is not particularly interesting, I'm trying to fine tune the parameters into pol51 a bit. The suggested parameters from ggnfs's def-nm-params.txt seem to result in way too many lines output from pol51m0b, so that pol51opt takes way too long.

- ben.

fivemack · 2008-10-03, 15:32

sean: that's a fine piece of work!

I can't find a recently-updated site with the factorial factors in; http://www.leyland.vispa.com/numth/f...factorial-.txt still has 120!-1 with a C127 cofactor. Do you know of one?

sean · 2008-10-05, 20:02

Quote:

Originally Posted by fivemack

sean: that's a fine piece of work!

I can't find a recently-updated site with the factorial factors in; http://www.leyland.vispa.com/numth/f...factorial-.txt still has 120!-1 with a C127 cofactor. Do you know of one?

Yep, I finished that one in 2004. Here is the known results in range of interest.
Paul and Andrew haven't updated their sites for a long time.

Code:

n!-1 for 109 <= n <= 135

109!-1 199.124447.15824252755580629.2393584415705844388207.P132
110!-1 90533.679735247.291374596607656314829.P144
111!-1 113.223.619.22079.77515433.71907484857881021.55353226459576651599997.P122
112!-1 571.571.790772324341378194783917.549585323219368602369820121.P127
113!-1 3343239143.807281173211.112653507736977123212855475998117625287101801671405101833429.P104
114!-1 46592495579025763749447076981.156548140613622977981626666310401198875601601.10651838022424183034932542865787273875648790960999.P65
115!-1 21839.2654065788714484499.P166
116!-1 45353623723271.7249738248311668783.2441600989787695967962441.629568685143887122306747853927.60142427312522623487250730465114097841091.P64
117!-1 199.414299629571.10596188107801343.38197980429736991738205655885367.P132
118!-1 3257.18457.2834309.559478453.3339546779.93860151591549156672389.P140
119!-1 239.1238749.612038098439.19949663277967.593016762123272567713327930159.135075706114535316950231097516031.P102
120!-1 137.566161495146584181973.174568885579274269812937093465102210976297.51442741042891005984634751109466441839162295178987.P85
121!-1 449.9019468366543187582693440693767816128108542844167.P150
122!-1 139.1381.86931787124894025899613982958574289.5576508736105627548402879357332051369062018458499320479330647748552094650266337.P85
123!-1 149.12601.1048668380909.565310453158799.150152322348158556906709.546438722226889371614324889973.649887067848818772887462916835461246603936294119701.P69
124!-1 774577.1371619964001615151511.48377627659132602412103759.P155
125!-1 127.251.5669.1990086482671125913.2007083736859170236448088811.27540617119625946118459403939.P127
126!-1 52147.8035604011121317.P191
127!-1 28087.314264884421286209.134013277989741695639179.4975560684609281103633431477.5397554794221433215092107232321743.67713346982387980795461394231203640841.P70
128!-1 797.1147463.96219075145726707178129001299019.P175
129!-1 131.359.919.1675932179.188688334348298185613260389556326587556468251.P157
130!-1 29033.1443754424824480405672165207097.10498667669119496541246764547364394150767.P146
131!-1 233.12893.388797000863.767761264702576031559515348521.C174
132!-1 503.491923.7281977.4139884411675565479171577.C185
133!-1 829.2459843.216813557.370071375566251.1556151131905519619.513047728616968716016761833299351.P144
134!-1 3227027.4879729.32442129901367.P202
135!-1 137.271.6949.3570539239.66033127812014946343.P193

n!+1 for 109 <= n <= 135

109!+1 C177
110!+1 1907.59852621142437.1131669878120932220109197009.12365412673468289639313600923.984858384210167262655808345015050645243243.P65
111!+1 2626395763.21817665100657487402784047413.366490840976610304104746977769369661622517455940520616223381.P83
112!+1 113.109799165627.7001254410846736563763702929325048987.5651878146949530735523997358628882351147.161785206248676056929457299898406991572743.P52
113!+1 227.5693839.4554665692949825778957079924193.440329859646244565885691592803661547.P109
114!+1 C187
115!+1 C189
116!+1 P191
117!+1 20454945767189.7608449170252404294833488675127.P149
118!+1 46757.82219.1871263.11294645177647665140920980967.26722464573695888110450933578985133184055013159596413387712641189727401257.P78
119!+1 1188269.241580277689.39791036138857.C166
120!+1 12149.288790123.19236668797.258847257209.25829710930321439085184019803339.P134
121!+1 214147.589577851.33194658402572018837993.1744502186874309020303267203.11888627126804025025004652051467258556118244612927.P88
122!+1 359.1003874788568233.C186
123!+1 887.316189.7132885373707342182361401607765717.P163
124!+1 2671.68428636341940746996456551633.29455596869306730157787712690502974736104077.P132
125!+1 28735807.1311489401499009659.C184
126!+1 127.755326181.494773752852444988003703.421253711938605020303598673.656744471822428154156989986023329307044463.P109
127!+1 3407.5087.8179.7500502393.557262536830523.14390547767773598982217841964761.2002896480650155684677061635571976457061002571505493757461762604981.P81
128!+1 401.5791.389539.C204
129!+1 683.178151.4111591543.580521735671.8757563510467.C176
130!+1 131.29879.C214
131!+1 263.14858314567.107067562961.C199
132!+1 3049.39688194769.126701555548860527771595243471901442557649471.P166
133!+1 9936338092981.5589740040117928890400907674537.P183
134!+1 34031.2155409.6164890522139.2396398255928539.225377192789914071606361.P166
135!+1 631.33791809.57036179.1258996199.25171760610077.68685878668312253297137563108870264189563273.251117463176562003602241435134677475066949277.P102

A reasonable up-to-date list of factors can be obtained from here:

http://groups.yahoo.com/group/primef...0080407.txt.gz

sean · 2008-10-05, 20:08

Quote:

Originally Posted by bsquared

T
If you remember, can you say anything about what parameters you used for polynomial selection, assuming you used pol51*?

- ben.

I've run a lot of GNFS jobs around C145. In general, I use the following formulas to select parameters to pol51*. Let L be the length of the composite, then I use

normmax = 0.001788979 * exp(0.395898 * L);
normmax1 = 0.003586924 * exp(0.361666 * L);
normmax2 = 0.000364483 * exp(0.340319 * L);
murphymax = 0.001658668 * exp(-0.133841 * L);

From memory, I came up with these numbers by curve fitting some earlier runs. I have used these from jobs in the range C107 to C163. I definitely wouldn't claim they are optimal in any sense, but seem to work quite well in practice.

I'm not sure how this compares with GGNFS.

bsquared · 2008-10-05, 22:11

Quote:

Originally Posted by sean

From memory, I came up with these numbers by curve fitting some earlier runs.

I am going through just such as exercise now, and am trying to expand my data set (and thus confidence in the fit). With 9 data point ranging from C121 to C180, my curves are:

normmax = 1.553287*exp(0.345707*L)
normmax1 = 0.00120734*exp(0.371633*L)
normmax2 = 0.0000705407*exp(0.352842*L)
murphymax = 0.00274959*exp(-0.13783871*L)

So I'm just fishing for more data...

- ben.

xilman · 2008-10-06, 08:46

Quote:

Originally Posted by sean

Yep, I finished that one in 2004. Here is the known results in range of interest. Paul and Andrew haven't updated their sites for a long time.

I tend to update my tables when people update me. That is, unless I'm actively working on something I tend not to seek out progress made elsewhere.

Now you've drawn the situation to my attention, and provided factor tables, I'll see what I can do.

Paul

2008-10-02, 01:19	#38
sean Aug 2004 New Zealand 230₁₀ Posts	C163 GNFS I have completed the factorization of 122!-1 by GNFS. On 2000-02-11 David Miller found the factor 86931787124894025899613982958574289, leaving a C163. It took me 5 months with the Franke, Kleinjung, Bahr, et al. implementation of GNFS to complete the factorization of this number. This is my personal best for GNFS. Code: 122!-1 139.1381.86931787124894025899613982958574289.5576508736105627548402879357332051369062018458499320479330647748552094650266337.P85 The config file was: Code: 5917686603831398223364673435358357137280652296278084434087991373071815772650029267347702479825598785894524590493753852303353769977519673999810345326389649459944649 X5 1442880 X4 -16901347639083 X3 -8587858228985321843 X2 43202270329828664385398008 X1 -2656547829320952529053251445729 X0 -16135033462316010115027001103203281449 Y1 14865695238506713 Y0 -21017659422567500102090287663966 M 2341541861803943155263839678058508653484076369623228078635782207837116358579684473849075085246884117912305105122625113706595271848522729665000121875538951988596057 0 11000000 2.8 32 62 0 21000000 2.8 32 62 Sieving took 1.5 months on a variety of machines. The rest of the time was taken by the post-processing including the Lanczos reduction of a 8.8M matrix using my own Java port of the Franke lanczos code. The reduction was performed on a dual-core 1.8 MHz Opteron with 16GB of RAM. The smallest n of the form n!-1 not yet completely factored is 131!-1. On the + side, 109!+1 still resists my best efforts with ECM. The smallest composite of these forms not yet factored is 144!+1 C163.

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2008-10-01, 16:55	#34
themaster Dec 2007 27₁₀ Posts	3125816322396491327908016847491033937128894943594234816697681006021363321771944734880578361789769904775235680462891977712703 = 23059 x 479274976453780697 (Curve 31) x 1009436544491716921163 (Curve 57) x 430197652347851365324169 (Curve 332) x 4556941504336643669106130417 x 142928131963475091552029641439 (SIQS) quite a nice number of medium size factors

2008-10-01, 17:45	#35
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3·7·479 Posts	Bruce and Greg did this monstrosity - http://mersenneforum.org/showpost.ph...&postcount=397

2008-10-01, 18:57	#37
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3×7×479 Posts	Quartics? Now, paraphrasing The Graduate infamous hint: "Septics!" __________ Mr. McGuire: I want to say one word to you. Just one word. Benjamin: Yes, sir. Mr. McGuire: Are you listening? Benjamin: Yes, I am. Mr. McGuire: Plastics. Benjamin: Just how do you mean that, sir?

2008-10-03, 13:46	#39
bsquared "Ben" Feb 2007 3,733 Posts	That's quite an effort sean, nice job! If you remember, can you say anything about what parameters you used for polynomial selection, assuming you used pol51*? I'm working on a C145 right now, and while the size of the number is not particularly interesting, I'm trying to fine tune the parameters into pol51 a bit. The suggested parameters from ggnfs's def-nm-params.txt seem to result in way too many lines output from pol51m0b, so that pol51opt takes way too long. - ben.

2008-10-03, 15:32	#40
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 2·7·461 Posts	sean: that's a fine piece of work! I can't find a recently-updated site with the factorial factors in; http://www.leyland.vispa.com/numth/f...factorial-.txt still has 120!-1 with a C127 cofactor. Do you know of one?