Polynomial Request Thread - Page 31

Batalov · 2013-11-10, 06:31

4788:c158, -- quite a spike:

Code:

# norm 3.771589e-15 alpha -7.044717 e 2.259e-12 rroots 5
skew: 2408232.54
c0: 2297126373038672701121178654414314160
c1: 22834862368849317559107944404584
c2: -13268823723297809933756990
c3: -16179228185053771085
c4: 2194397641582
c5: 529032
Y0: -2066996123388194327058650691191
Y1: 499502908585476829

I'll run it.

RichD · 2013-11-14, 03:52

Yet another Aliquout Sequence has arrived at the GNFS door step.

The last term is here.

The number is here.

And the number is:

Code:

13426200991428692169418381497825169027960461421490230502520347900514146969637877496279892920490293993706711416849297576344652891621399116270908074351466751737163

Thanks to all...

chris2be8 · 2013-11-16, 16:56

Two more from the Brent tables:
76^124+1
318733927042289467050110876453540803022281106961240822511041903044154859344057277649933097487742590946360879014857225161120143114767600816722681188165411481

96^113+1
354820650656377431976006511268540290296643470316322144184823035457241065014505054188432043373973704735292377684606097239279102490945957095795475676255064919

These are the last two 156 digit targets.

Thanks in advance.

Chris

Batalov · 2013-11-16, 19:02

For the second of them, {2*x^6+3, x=3^19*2^94} should be nearly as good as any GNFS poly (esp. with time for poly selection saved).

EDIT: well, some short-term selection turned up a few polys, and maybe there's value in it. I haven't test-sieved yet; that would be a litmus test. I am going to test-sieve these two, for experiment sake:

Code:

n: 354820650656377431976006511268540290296643470316322144184823035457241065014505054188432043373973704735292377684606097239279102490945957095795475676255064919
type: gnfs
# norm 3.702628e-15 alpha -6.359569 e 2.384e-12 rroots 3
skew: 15393209.66
c0: -362814960304650954404441362416112305174
c1: 71129337549020412075458367073903
c2: 7155929275602105183934210
c3: -471437945812937270
c4: 160005229224
c5: 72
Y0: -5476895497697141423683433167915
Y1: 23376863276505779
rlim: 33554431
alim: 33554431
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
#-------------------------------------------
n: 354820650656377431976006511268540290296643470316322144184823035457241065014505054188432043373973704735292377684606097239279102490945957095795475676255064919
type: snfs
# size 4.996e-11, alpha 1.523, combined = 2.043e-12 rroots = 0
Y1: 1
Y0: -23020960097885819359313910361623625728
c6: 2
c0: 3
skew: 1
rlim: 33554431
alim: 33554431
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6

EDIT 2: GNFS wins by a small margin (but time has to be spent to find a better poly). It also wins the other contenders: the 27*x^5+1 and x^5+9 polynomials.

EDIT 3: Here's a better poly:

Code:

# norm 4.429772e-15 alpha -8.111677 e 2.678e-12 rroots 5
skew: 76684363.15
c0: 25726212623526552039183520256224965442560
c1: 23179475190864056442908339312219408
c2: 586633603236906518312188056
c3: -15401518764460988115
c4: -80721438478
c5: 504
Y0: -3711214832628213848164307254741
Y1: 113367306240660979

wombatman · 2013-11-17, 03:36

Running on RichD's C161.

sashamkrt · 2013-11-17, 07:27

Code:

n: 13426200991428692169418381497825169027960461421490230502520347900514146969637877496279892920490293993706711416849297576344652891621399116270908074351466751737163
# norm 1.744657e-015 alpha -6.988965 e 1.408e-012 rroots 5
skew: 3705163.87
c0: -10026363544660207512737340770847361563
c1: 72438563414211920894474844808884
c2: 139600525313114885649927050
c3: 4742123042748599795
c4: -8952386483152
c5: 354756
Y0: -8233883016016177089479669252950
Y1: 50448339994664279

# norm 1.744222e-015 alpha -8.063181 e 1.406e-012 rroots 5
skew: 7608165.10
c0: -1588218305426190608700815064439393838160
c1: 1268113430489476568401769790084158
c2: 674194338301900582235485307
c3: -21125668241205759382
c4: -11575495239348
c5: 360360
Y0: -8208114038333943743100529851359
Y1: 201243521820748021

# norm 1.684410e-015 alpha -8.442898 e 1.366e-012 rroots 3
skew: 7471211.99
c0: -684281562668824994165683926181776587841
c1: -1282735896546399151593369647414532
c2: -390831730565242191020870879
c3: -83181784752514432168
c4: 14333681695780
c5: 327600
Y0: -8366076209895250444452007019650
Y1: 74460444859652977

# norm 1.680168e-015 alpha -7.846078 e 1.363e-012 rroots 5
skew: 6758284.94
c0: -688731575532952648886452285592189775120
c1: 719245651647995979773946187255158
c2: 652009921945177195571409707
c3: 35754541301850674858
c4: -13610123835348
c5: 360360
Y0: -8208114265582153453525610124979
Y1: 201243521820748021

76^124+1

Code:

n: 318733927042289467050110876453540803022281106961240822511041903044154859344057277649933097487742590946360879014857225161120143114767600816722681188165411481
# norm 4.640349e-015 alpha -6.836060 e 2.458e-012 rroots 3
skew: 11973691.87
c0: 144493261435043414917909362365182799400
c1: -147180762069566583639306231178137
c2: 23209170383681296606033977
c3: 6634776114574463125
c4: -61703186962
c5: 792
Y0: -3318491569035097136252920793197
Y1: 47179250647950731

wombatman · 2013-11-17, 16:31

Well, Sashamkrt beat the crap out of my best one, so I would use those ;)

chris2be8 · 2013-11-18, 16:57

Thanks for the polys, I'll probably start sieving tomorrow. And I'll note Batalov's comments on where the crossover between SNFS and GNFS is (there are a few that are probably quicker by GNFS).

Chris

Batalov · 2013-11-18, 17:35

In the range of sizes available to most people, SNFS should be faster when
length > diff._SNFS * 0.56 + 30.
(length = log₁₀C)

For this number these were practically equal:
155.5 vs. 155.4 (=224*0.56+30)

RichD · 2013-11-18, 22:09

I test sieved the first poly from sashamkrt to find the best parameters. Then I noticed the second one had a really close e-score. I test sieved that one and it sieved a bit better. I didn't go through the exercises of finding the parameters for the second poly, I just copied them from the first.

Siever 14e can be used for this number. I wonder if NFS@Home would be interested, else we can do a team sieve after the current number finishes.

Code:

# sieve with ggnfs lasieve4I14e on the -a side
# aq4788:5193
n: 13426200991428692169418381497825169027960461421490230502520347900514146969637877496279892920490293993706711416849297576344652891621399116270908074351466751737163
# norm 1.744222e-015 alpha -8.063181 e 1.406e-012 rroots 5
skew: 7608165.10
c0: -1588218305426190608700815064439393838160
c1: 1268113430489476568401769790084158
c2: 674194338301900582235485307
c3: -21125668241205759382
c4: -11575495239348
c5: 360360
Y0: -8208114038333943743100529851359
Y1: 201243521820748021
rlim: 50000000
alim: 50000000
lpbr: 30
lpba: 30
mfbr: 60
mfba: 60
rlambda: 2.5
alambda: 2.5

RichD · 2013-11-23, 02:00

Quote:

Originally Posted by RichD

… else we can do a team sieve after the current number finishes.

Posted to team sieve.

2013-11-14, 03:52	#332
RichD Sep 2008 Kansas 2⁴·211 Posts	AS 4788:i5193 (C161) Yet another Aliquout Sequence has arrived at the GNFS door step. The last term is here. The number is here. And the number is: Code: 13426200991428692169418381497825169027960461421490230502520347900514146969637877496279892920490293993706711416849297576344652891621399116270908074351466751737163 Thanks to all...

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2013-11-16, 16:56	#333
chris2be8 Sep 2009 2078₁₀ Posts	Two more from the Brent tables: 76^124+1 318733927042289467050110876453540803022281106961240822511041903044154859344057277649933097487742590946360879014857225161120143114767600816722681188165411481 96^113+1 354820650656377431976006511268540290296643470316322144184823035457241065014505054188432043373973704735292377684606097239279102490945957095795475676255064919 These are the last two 156 digit targets. Thanks in advance. Chris

2013-11-17, 03:36	#335
wombatman I moo ablest echo power! May 2013 1769₁₀ Posts	Running on RichD's C161.

2013-11-17, 16:31	#337
wombatman I moo ablest echo power! May 2013 29×61 Posts	Well, Sashamkrt beat the crap out of my best one, so I would use those ;)

2013-11-18, 16:57	#338
chris2be8 Sep 2009 2×1,039 Posts	Thanks for the polys, I'll probably start sieving tomorrow. And I'll note Batalov's comments on where the crossover between SNFS and GNFS is (there are a few that are probably quicker by GNFS). Chris

2013-11-18, 17:35	#339
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9478₁₀ Posts	In the range of sizes available to most people, SNFS should be faster when length > diff._SNFS * 0.56 + 30. (length = log₁₀C) For this number these were practically equal: 155.5 vs. 155.4 (=224*0.56+30)