GNFS targets which need more ECM - Page 22

Max0526 · 2017-03-25, 16:44

@swellman
After CADO manual therapy:

Code:

Y0: -129441582292879766852802142335913812852
Y1: 226800817851771043265593
c0: 127727595454181971071965592639564517403004873914410
c1: -442425314002868969398927726762880897840077
c2: -870316047967277613008667600606508
c3: 3133855843029980079905629
c4: 908208518625690
c5: 105000
skew: 1387995739.513
# lognorm 64.59, E 55.51, alpha -9.08 (proj -2.15), 1 real root
# MurphyE=7.60e-15

and also

Code:

Y0: -129441585338186965938273551145068641428
Y1: 226800817851771043265593
c0: 93194469791255244270684762652627818880592012087530
c1: -830544676240168320597354536005054309105813
c2: -995572445709087897900086634549076
c3: 3085266242181267151945309
c4: 901159221825690
c5: 105000
skew: 1531159316.085
# lognorm 64.66, E 55.78, alpha -8.88 (proj -2.15), 3 real roots
# MurphyE=7.31e-15

VBCurtis · 2017-03-25, 18:17

Quote:

Originally Posted by Max0526

@swellman
Progress so far. You may start sieving. :)

well, no, he cannot start sieving until a final poly is chosen. He can't even test-sieve, because different GNFS polys respond differently to parameter choices; though a test of 15/33 vs 16/33 may already be useful on your best-found so far. This may be a case where the grid does 15/33 while a few outside users do 16/33 on a specific Q-range left off the grid and send relations manually to whomever does the matrix; my experience is that different q-ranges have different relative advantages in sec/rel for 16e vs 15e, and we may choose to leverage that to extend the usefulness of the 15e grid.

swellman · 2017-03-25, 21:49

Quote:

Originally Posted by VBCurtis

well, no, he cannot start sieving until a final poly is chosen. He can't even test-sieve, because different GNFS polys respond differently to parameter choices; though a test of 15/33 vs 16/33 may already be useful on your best-found so far. This may be a case where the grid does 15/33 while a few outside users do 16/33 on a specific Q-range left off the grid and send relations manually to whomever does the matrix; my experience is that different q-ranges have different relative advantages in sec/rel for 16e vs 15e, and we may choose to leverage that to extend the usefulness of the 15e grid.

While I don't disagree with your premise, this is really just a matter of settling whether to use SNFS or GNFS, and on which siever to do it. I plan on running some comparative test sieving on Max's poly results as discussed here. Presumably yield and speed results will settle the 15e or 16e question, as well as whether the best GNFS poly beats the best of the SNFS (which I believe is the case).

Optimizing the parameters for the full sieving is another issue.

VBCurtis · 2017-03-25, 23:18

Ah, yes, I forgot the SNFS score is a sextic, and not directly comparable to GNFS quintic score. I had assumed the GNFS choice was settled. Whoops!

Sorry, Max. :)

Max0526 · 2017-03-26, 19:07

@swellman
Good news from CADO -- E score broke into 8s:

Code:

Y0: -66639466470090969807796083294200781193
Y1: 34237568437838650288907
c0: -20651639625122894646111316805227359185476502909040
c1: 218676039845425136144283051205405397193958
c2: 1734492569001794961072674562370809
c3: -1253915992353438586882365
c4: 1346104891740278
c5: 580680
skew: 1096958438.913
# lognorm 64.61, E 55.53, alpha -9.08 (proj -1.68), 3 real roots
# MurphyE=8.04e-15

Also, for variety:

Code:

Y0: -66639453492857777678740806257966082521
Y1: 34237568437838650288907
c0: -124746226958990451672542162967484126973938369313040
c1: -1424630955676256999193848308047991051921542
c2: 1785218167494878837354831950862637
c3: 1621215080743493238430787
c4: 2446594808786678
c5: 580680
skew: 1548192245.668
# lognorm 65.57, E 56.19, alpha -9.37 (proj -1.68), 3 real roots
# MurphyE=7.75e-15

Code:

Y0: -66639482359801809719309229634806354905
Y1: 34237568437838650288907
c0: -1884388613277380522296017451718998493044909216489296
c1: 2628791210679606654441584967800296862850738
c2: 4639485798726882957623338420476357
c3: -2502105362646182512538557
c4: -1367740154122
c5: 580680
skew: 1926494519.675
# lognorm 65.62, E 56.16, alpha -9.45 (proj -1.68), 3 real roots
# MurphyE=7.55e-15

Code:

Y0: -87512176913405978269547228860243497470
Y1: 30649333633905789572191
c0: -1195215493847402487378903065035504506150364173289962
c1: 15424204579642900771676891422862836106823851
c2: 2959489139254893168718355325539718
c3: -8010192758420315533601111
c4: -273772437186576
c5: 892080
skew: 2130264898.026
# lognorm 66.23, E 56.30, alpha -9.93 (proj -2.44), 3 real roots
# MurphyE=7.52e-15

Code:

Y0: -66639463986312050755773554497719969625
Y1: 34237568437838650288907
c0: -50298858452399587964299032713682580368351085305576
c1: 144799430030110404897576903198972873059938
c2: 1506318127803862982825408105527437
c3: -832740741020882914054077
c4: 1556733275781878
c5: 580680
skew: 1050096169.182
# lognorm 64.58, E 55.86, alpha -8.72 (proj -1.68), 3 real roots
# MurphyE=7.43e-15

Code:

Y0: -61881950263661702152389115243050546195
Y1: 68134761333096744986009
c0: -45349947802638640816692477948822822284002749800
c1: 6217143237750368971199977188293405471866
c2: 53127777849688549554251259285503
c3: -936680344984278768153163
c4: -1578764735260425
c5: 2102400
skew: 296728517.214
# lognorm 62.50, E 55.68, alpha -6.82 (proj -1.61), 5 real roots
# MurphyE=7.37e-15

Code:

Y0: -76982023423812158314219881849466659154
Y1: 670031662708665115953343
c0: -6093042239063245341356018687452765193152865442775
c1: -86229859386518836875324612745099034218375
c2: -138098301473181052470230963918939
c3: 9077784650120915518918327
c4: 3334109274161826
c5: 423360
skew: 1234086197.934
# lognorm 65.71, E 56.56, alpha -9.15 (proj -2.37), 1 real root
# MurphyE=7.32e-15

Max0526 · 2017-03-26, 20:18

@swellman
I am done for now. That should be enough to test-sieve and compare GNFS to SNFS.
I will also post E=8.04*10^-15 poly as a current record.
Let me know.

Code:

R0: -66639499539531673701030636533234216372
R1: 34237568437838650288907
A0: -12902918709469751148237632201212514994409956655799202
A1: -3732419154040322217176132466326185779786519
A2: 7670309385553992522043823931440256
A3: -1037305169294486407548229
A4: -1458236027329522
A5: 580680
skew 2214641428.89, size 2.968e-019, alpha -10.004, combined = 7.895e-015 rroots = 3

Code:

# norm 3.301585e-019 alpha -7.199832 e 7.625e-015 rroots 5
skew: 287641325.17
c0: -574895525937352524602338208472098702376437680181
c1: 14429620591842064101638761292252480466163
c2: 219075169379313217664562469069106
c3: -64221985543193871734263
c4: -2660477255404425
c5: 2102400
Y0: -61881957274908314693679550419904751928
Y1: 68134761333096744986009

Code:

# norm 3.295338e-019 alpha -9.513460 e 7.579e-015 rroots 3
skew: 1702823321.25
c0: -3008433535350404847712336028554376432278676404803000
c1: 1132141910843117234844720594548753357179330
c2: 5706698930666640730820205990682071
c3: -2380010287829962723055181
c4: -421007471220922
c5: 580680
Y0: -66639487308291171032173802303962380019
Y1: 34237568437838650288907

Code:

# norm 3.243810e-019 alpha -9.116151 e 7.497e-015 rroots 3
skew: 1236237847.33
c0: -370597353327856651991044361747788873248007269260250
c1: 399284002759424639638378575743062254379233
c2: 3285292506292642175940406522983192
c3: -2303755369932123915763333
c4: 536606517977678
c5: 580680
Y0: -66639476015884168132556273444352726716
Y1: 34237568437838650288907

Code:

# norm 3.182377e-019 alpha -7.051638 e 7.479e-015 rroots 5
skew: 266266212.35
c0: -304048188129972270641598964995030434246667065568
c1: 12382335515680511166476793167404971381092
c2: 132883492015500800172735606570257
c3: -712269703651308811048363
c4: -1916246440348425
c5: 2102400
Y0: -61881952451088969128932249293757550011
Y1: 68134761333096744986009

Code:

# norm 3.250752e-019 alpha -9.709993 e 7.415e-015 rroots 5
skew: 1967050183.36
c0: 2245263846864016529799888118602794609159307930142728
c1: 14700819319254092131071763410635845869658874
c2: -4994065505488612168008708069297177
c3: -7363857238774453971764279
c4: 1231425524860224
c5: 892080
Y0: 87512166570541095333613819719911682673
Y1: -30649333633905789572191

Code:

# norm 3.207639e-019 alpha -8.769752 e 7.409e-015 rroots 3
skew: 951473460.80
c0: -101262026204377649407496677906777731811967952212376
c1: -53494194621247370536025052284472805866662
c2: 1696221648089536471555129433485287
c3: -1197245515997570568827277
c4: 1376323693791878
c5: 580680
Y0: -66639466113743823926707011027135346075
Y1: 34237568437838650288907

Code:

# norm 3.277995e-019 alpha -9.607382 e 7.403e-015 rroots 5
skew: 1749768504.27
c0: -2460995798499146011208884828526199252600972502855800
c1: 11143403357619007712825843177135698628924810
c2: -9721505750178874285460843427922821
c3: -5681695324591880305584695
c4: 2295205072381824
c5: 892080
Y0: 87512159260852667184825124708718601709
Y1: -30649333633905789572191

Code:

# norm 3.166312e-019 alpha -7.001592 e 7.400e-015 rroots 5
skew: 266224277.60
c0: 92120826109262922940519398410839822141455335944
c1: 12754762991805047354932155370128745209658
c2: 200196543289229123482296529203581
c3: -358492326367488543829363
c4: -2351904401788425
c5: 2102400
Y0: -61881955274857160298820445917066364841
Y1: 68134761333096744986009

Code:

# norm 3.140496e-019 alpha -6.819467 e 7.379e-015 rroots 5
skew: 211223751.87
c0: -84665580236732850177599785816739710094907555195
c1: 5372374029296091073038103500343594872371
c2: 71685076375010598464092557561008
c3: -893027853404098055251663
c4: -1649828956300425
c5: 2102400
Y0: -61881950724272788518716374888242258850
Y1: 68134761333096744986009

swellman · 2017-03-26, 21:17

Thank you Max for all your effort. I'll run some test sieving on Tuesday. I expect this will be a 33-bit job on 15e. I'll run blocks of 10000 Q for 2-3 starting values of Q for all the polys. Smaller blocks for 3LP testing to keep things sane.

Max0526 · 2017-03-27, 23:17

@swellman
A couple more CADO optimizations. Some Es are duplicated but alphas are new.

Code:

Y0: 87512145467397012624240500458733369585
Y1: -30649333633905789572191
c0: 261089349290322119644339590008606175878263149269448
c1: -39205033260298478979057105155177339891014
c2: -13790180855074264355235276076330137
c3: 256840792273365250325449
c4: 4302567788207424
c5: 892080
skew: 1853339554.534
# lognorm 66.21, E 56.30, alpha -9.92 (proj -2.44), 5 real roots
# MurphyE=7.91e-15

Code:

Y0: -61881959937567910875303173912586097736
Y1: 68134761333096744986009
c0: -806789015722600171468824051695294504291623527909
c1: -2327587355477229624386233984702886302797
c2: 200971308188333504773533642915074
c3: 383764195165512635544137
c4: -3071278983148425
c5: 2102400
skew: 343484091.734
# lognorm 63.18, E 55.98, alpha -7.20 (proj -1.61), 5 real roots
# MurphyE=7.61e-15

Code:

Y0: -66639486966213319261628057833755582012
Y1: 34237568437838650288907
c0: -28612468910685561826332308610506781999759107100122
c1: 1245460667350046377321360213518805863312641
c2: 5635114359626790157543254735918696
c3: -2396256267130479340366469
c4: -391998727897522
c5: 580680
skew: 1486459816.276
# lognorm 65.07, E 55.78, alpha -9.29 (proj -1.68), 3 real roots
# MurphyE=7.59e-15

Code:

Y0: -66639484292220878189779090981795306172
Y1: 34237568437838650288907
c0: -1314059861019414620549779128678398469549308667151002
c1: 2081189971805161556729171054411250083352081
c2: 5062083176912081235970498810702056
c3: -2483298194659862944145029
c4: -165239936089522
c5: 580680
skew: 1845722373.027
# lognorm 65.51, E 56.06, alpha -9.45 (proj -1.68), 3 real roots
# MurphyE=7.58e-15

another alpha:

Code:

Y0: -66639479449321924055199245574793203315
Y1: 34237568437838650288907
c0: -2776564335368063041279555931311952461809737860835936
c1: 3363486494235827696869116924019196299131818
c2: 4004893954795192811704959805459287
c3: -2460608047187997945623117
c4: 245445561303878
c5: 580680
skew: 2078892959.571
# lognorm 65.82, E 56.30, alpha -9.52 (proj -1.68), 3 real roots
# MurphyE=7.55e-15

Code:

Y0: -61881952708550064317350251959369702347
Y1: 68134761333096744986009
c0: -348901940184068322955275239607751121452814479392
c1: 11347985803655378076242107642728401190212
c2: 140792558864810709695881565790113
c3: -683005797925981384499563
c4: -1955968176796425
c5: 2102400
skew: 361795633.691
# lognorm 62.89, E 55.84, alpha -7.05 (proj -1.61), 5 real roots
# MurphyE=7.45e-15

another alpha:

Code:

Y0: -61881949653841824999383962075782822377
Y1: 68134761333096744986009
c0: -1987336593057611763019989423911876114067886689480
c1: 33671594679458698968824073698386462294026
c2: 27233574751210280634608795464637
c3: -991517247169071010280563
c4: -1484680211836425
c5: 2102400
skew: 378440062.096
# lognorm 62.94, E 55.97, alpha -6.97 (proj -1.61), 5 real roots
# MurphyE=7.37e-15

Max0526 · 2017-03-28, 01:51

@swellman

Code:

# norm 3.355559e-019 alpha -7.378994 e 7.587e-015 rroots 3
skew: 302830431.30
c0: 1068703205381284825252876873400771747721808810728
c1: 26409636535828996095254344668452434689242
c2: 210866407548859511571353444019683
c3: 259932134695426471876037
c4: -2963425936732425
c5: 2102400
Y0: -61881959238505736541059902033348659799
Y1: 68134761333096744986009

swellman · 2017-03-28, 02:52

Thank you Max for all the work. Certainly not half-hearted! I am reminded of the old adage - careful what you wish for, you just might get it.

It will take me a few days to chew through all the polys.

swellman · 2017-04-01, 00:29

Still test sieving and progress is slow. Using an old machine, and running 10,000 Q on the algebraic side at two different starting Q values for each poly. Takes 1-3 hours to complete each run. And Max found 29 polys. But honor (and prudence) demands a thorough sieving investigation.

The effort may be incomplete but two facts have surfaced:

- GNFS is much faster than SNFS for this composite
- the highest e-score found by Max (8.04e-15) has so far proven to be the best sieving poly (though there are still lot of polys to be tested)

Hi ho hi ho, back to sieving we go...

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2017-03-25, 23:18	#235
VBCurtis "Curtis" Feb 2005 Riverside, CA 4,861 Posts	Ah, yes, I forgot the SNFS score is a sextic, and not directly comparable to GNFS quintic score. I had assumed the GNFS choice was settled. Whoops! Sorry, Max. :)

2017-03-26, 21:17	#238
swellman Jun 2012 2²·13·59 Posts	Thank you Max for all your effort. I'll run some test sieving on Tuesday. I expect this will be a 33-bit job on 15e. I'll run blocks of 10000 Q for 2-3 starting values of Q for all the polys. Smaller blocks for 3LP testing to keep things sane.

2017-03-28, 02:52	#241
swellman Jun 2012 2²·13·59 Posts	Thank you Max for all the work. Certainly not half-hearted! I am reminded of the old adage - careful what you wish for, you just might get it. It will take me a few days to chew through all the polys.

2017-04-01, 00:29	#242
swellman Jun 2012 BFC₁₆ Posts	Still test sieving and progress is slow. Using an old machine, and running 10,000 Q on the algebraic side at two different starting Q values for each poly. Takes 1-3 hours to complete each run. And Max found 29 polys. But honor (and prudence) demands a thorough sieving investigation. The effort may be incomplete but two facts have surfaced: - GNFS is much faster than SNFS for this composite - the highest e-score found by Max (8.04e-15) has so far proven to be the best sieving poly (though there are still lot of polys to be tested) Hi ho hi ho, back to sieving we go...