Polynomial Request Thread

[swellman]

Early run with CADO:

 n: 5010968787585504607949192210942377079379285178590004729749207487507787040684433640392691082409304410877720888569557186261540033154512666518900413521876524079689418720554031235001
skew: 65822261.973
c0: 248436776854993625508958637808607292507405067
c1: -12462770400853891584348157076891066001
c2: -179595227389142586823264059632
c3: 2361850744860258071051
c4: 77272871414325
c5: 66150
Y0: -51813769748585773738086070255988734
Y1: 630887621067686554708361
# MurphyE (Bf=4.295e+09,Bg=2.147e+09,area=2.416e+16) = 1.612e-08
# f(x) = 66150*x^5+77272871414325*x^4+2361850744860258071051*x^3-179595227389142586823264059632*x^2-12462770400853891584348157076891066001*x+248436776854993625508958637808607292507405067
# g(x) = 630887621067686554708361*x-51813769748585773738086070255988734

Cownoise says skew of 92836373.33244 gives an e-score of 1.00285063e-13, which is not good. Maybe it can be spun up?

CADO is still searching…

[Max0526]

Originally Posted by charybdis

2,1455+ is difficulty 234 with a quartic, which should be substantially faster than 190-digit GNFS. Curtis said a while back that he was going to run it; would be worth asking about his progress before reserving.

There are three spun polys found for this number with a slightly better score than the original found by yafu. Some test-sieving to consider.

Line 1 : {'c4': '1', 'c3': '-6', 'c2': '-4', 'c1': '24', 'c0': '16', 'Y1': '-79228162514264337593543950336', 'Y0': '25108406941546723055343157692989121989437950453043225952257'}

n: 1048986109490999718821031158099803559156220834780127548605119979970202887417617297259136595934074295495556093763001044549039558502774476460066588744646951315998860141075555780475360418938001
# e = 3.66341913e-14
skew: 3.49114
type: snfs
c4: 1
c3: -6
c2: -4
c1: 24
c0: 16
Y1: -79228162514264337593543950336
Y0: 25108406941546723055343157692989121989437950453043225952257

Line 2 : {'c4': '1', 'c3': '2', 'c2': '-16', 'c1': '-32', 'c0': '16', 'Y1': '-79228162514264337593543950336', 'Y0': '25108406941546723055343157692830665664409421777856138051585'}

n: 1048986109490999718821031158099803559156220834780127548605119979970202887417617297259136595934074295495556093763001044549039558502774476460066588744646951315998860141075555780475360418938001
# e = 3.6531355e-14
skew: 3.90799
type: snfs
c4: 1
c3: 2
c2: -16
c1: -32
c0: 16
Y1: -79228162514264337593543950336
Y0: 25108406941546723055343157692830665664409421777856138051585

Line 3 : {'c4': '1', 'c3': '-3', 'c2': '-1', 'c1': '3', 'c0': '1', 'Y1': '-158456325028528675187087900672', 'Y0': '25108406941546723055343157692989121989437950453043225952257'}

n: 1048986109490999718821031158099803559156220834780127548605119979970202887417617297259136595934074295495556093763001044549039558502774476460066588744646951315998860141075555780475360418938001
# e = 3.64484042e-14
skew: 1.74941
type: snfs
c4: 1
c3: -3
c2: -1
c1: 3
c0: 1
Y1: -158456325028528675187087900672
Y0: 25108406941546723055343157692989121989437950453043225952257

Original:

Line 1 : {'c4': '1', 'c3': '-4', 'c2': '-4', 'c1': '1', 'c0': '1', 'y1': '25108406941546723055343157692830665664409421777856138051585', 'y0': '-158456325028528675187087900672'}
Skew, Murphy E:
0.51085 3.63475871e-14

[swellman]

Wow! Finally got decent poly for the C178 of @connected’s post #1981 earlier in this thread:

n: 5010968787585504607949192210942377079379285178590004729749207487507787040684433640392691082409304410877720888569557186261540033154512666518900413521876524079689418720554031235001
skew: 7924630.129
c0: 16169846341318139364012308029717208260097
c1: 12751430081170197232277151268956955
c2: 712058615715448803602419384
c3: -489803879032484011081
c4: 5587786845045
c5: 1302000
Y0: -28632061087287122004388923355407648
Y1: 271486670024325210304109
# MurphyE (Bf=4.295e+09,Bg=2.147e+09,area=2.416e+16) = 1.865e-08
# f(x) = 1302000*x^5+5587786845045*x^4-489803879032484011081*x^3+712058615715448803602419384*x^2+12751430081170197232277151268956955*x+16169846341318139364012308029717208260097
# g(x) = 271486670024325210304109*x-28632061087287122004388923355407648
# cownoise: 1.24188261e-13 with skew of 9258484.57055

I’m done with this search.

[Max0526]

Originally Posted by swellman

Wow! Finally got decent poly for the C178 of @connected’s post #1981 earlier in this thread:

n: 5010968787585504607949192210942377079379285178590004729749207487507787040684433640392691082409304410877720888569557186261540033154512666518900413521876524079689418720554031235001
skew: 7924630.129
c0: 16169846341318139364012308029717208260097
c1: 12751430081170197232277151268956955
c2: 712058615715448803602419384
c3: -489803879032484011081
c4: 5587786845045
c5: 1302000
Y0: -28632061087287122004388923355407648
Y1: 271486670024325210304109
# MurphyE (Bf=4.295e+09,Bg=2.147e+09,area=2.416e+16) = 1.865e-08
# f(x) = 1302000*x^5+5587786845045*x^4-489803879032484011081*x^3+712058615715448803602419384*x^2+12751430081170197232277151268956955*x+16169846341318139364012308029717208260097
# g(x) = 271486670024325210304109*x-28632061087287122004388923355407648
# cownoise: 1.24188261e-13 with skew of 9258484.57055

I’m done with this search.

Can't spin it up sorry, the one below is just for EdH's run in CADO and/or to serve as another potential test-sieving candidate:

Line 1 : {'c5': '1302000', 'c4': '8763364845045', 'c3': '-475802895443632207081', 'c2': '4768513729845046773283984', 'c1': '13099432596011698410643565691867355', 'c0': '22502927551505175064314385264234413469097', 'Y1': '271486670024325210304109', 'Y0': '-28631928656089484138551337011037448'}

n: 5010968787585504607949192210942377079379285178590004729749207487507787040684433640392691082409304410877720888569557186261540033154512666518900413521876524079689418720554031235001
# e = 1.24206341e-13
skew: 9306589.88699
type: gnfs
c5: 1302000
c4: 8763364845045
c3: -475802895443632207081
c2: 4768513729845046773283984
c1: 13099432596011698410643565691867355
c0: 22502927551505175064314385264234413469097
Y1: 271486670024325210304109
Y0: -28631928656089484138551337011037448

[EdH]

Originally Posted by Max0526

Can't spin it up sorry, the one below is just for EdH's run in CADO and/or to serve as another potential test-sieving candidate:

Line 1 : {'c5': '1302000', 'c4': '8763364845045', 'c3': '-475802895443632207081', 'c2': '4768513729845046773283984', 'c1': '13099432596011698410643565691867355', 'c0': '22502927551505175064314385264234413469097', 'Y1': '271486670024325210304109', 'Y0': '-28631928656089484138551337011037448'}

n: 5010968787585504607949192210942377079379285178590004729749207487507787040684433640392691082409304410877720888569557186261540033154512666518900413521876524079689418720554031235001
# e = 1.24206341e-13
skew: 9306589.88699
type: gnfs
c5: 1302000
c4: 8763364845045
c3: -475802895443632207081
c2: 4768513729845046773283984
c1: 13099432596011698410643565691867355
c0: 22502927551505175064314385264234413469097
Y1: 271486670024325210304109
Y0: -28631928656089484138551337011037448

I've got both whirling as I write this. . .

[swellman]

Originally Posted by frmky

Sam asked NFS@Home to complete the following five numbers by GNFS, so I thought it best to ask for polynomials from the world experts. These will make "easy" numbers for the lasievef queue. Anyone up for the task?

c190  2,1455+ 1048986109490999718821031158099803559156220834780127548605119979970202887417617297259136595934074295495556093763001044549039558502774476460066588744646951315998860141075555780475360418938001
c192  2,1437- 611107371163848421820450973821345480342912300580293057960322683739827190178101343864102334349705870623975708441513871815511725498435007084961435584007401776001674040834367795099214461176740407
c192  2,1404+ 304845455794257065968778054531074759358711982352774480446619591856836978726981611743504947591028279725109172165580298172672756192472041207653814344520508304324640842761215954476264945447966881
c193  2,2630M 2610587447312528299715041475419278187423084811629780057699696244539734380123086185107934590397221603551592962786504074063152741766781043206936800788048509610853301701793190659924283494241022521
c197  2,2870M 12716446239242105384495886223778969972137929286896767990486922119587563031946761939676139388232272824975631515451161724723244328908683599379523797308580938394307415777602492415472684926177574622941

I’m assuming 2,1455+ is being factored via SNFS, so I’m starting a poly search for c192 2,1437- using msieve-GPU. Now searching c5 < 500K.

Hope others join in. These four poly searches could take a long time…

[VBCurtis]

Originally Posted by swellman

I’m assuming 2,1455+ is being factored via SNFS, so I’m starting a poly search for c192 2,1437- using msieve-GPU. Now searching c5 < 500K.

Hope others join in. These four poly searches could take a long time…

2,1455+ is finished. I PM'ed the factors to Greg today, since I am lazy and didn't bother to look up Dr Wagstaff's contact info.

[EdH]

Originally Posted by EdH

I've got both whirling as I write this. . .

This is odd to me. Unless someone can see something I don't, the two separate machines running two separate polys (one each), came back with identical results:

n: 5010968787585504607949192210942377079379285178590004729749207487507787040684433640392691082409304410877720888569557186261540033154512666518900413521876524079689418720554031235001
Y0: -28632061087287122004388923355407648
Y1: 271486670024325210304109
c0: 16169846341318139364012308029717208260097
c1: 12751430081170197232277151268956955
c2: 712058615715448803602419384
c3: -489803879032484011081
c4: 5587786845045
c5: 1302000
skew: 7924630.129
# lognorm 52.90, E 47.61, alpha -5.29 (proj -1.80), 5 real roots
# MurphyE(Bf=1.000e+07,Bg=5.000e+06,area=1.000e+16)=1.239e-13

cownoise:  9258484.57055    1.24188261e-13

n: 5010968787585504607949192210942377079379285178590004729749207487507787040684433640392691082409304410877720888569557186261540033154512666518900413521876524079689418720554031235001
Y0: -28632061087287122004388923355407648
Y1: 271486670024325210304109
c0: 16169846341318139364012308029717208260097
c1: 12751430081170197232277151268956955
c2: 712058615715448803602419384
c3: -489803879032484011081
c4: 5587786845045
c5: 1302000
skew: 7924630.129
# lognorm 52.90, E 47.61, alpha -5.29 (proj -1.80), 5 real roots
# MurphyE(Bf=1.000e+07,Bg=5.000e+06,area=1.000e+16)=1.239e-13

cownoise:   9258484.57055     1.24188261e-13

[VBCurtis]

Originally Posted by swellman

I’m assuming 2,1455+ is being factored via SNFS, so I’m starting a poly search for c192 2,1437- using msieve-GPU. Now searching c5 < 500K.

Hope others join in. These four poly searches could take a long time…

I've started CADO poly select for 2_1437-.
Parameters:
P=4 million
admin 15k, admax 300k, incr 210
nq = 15625

This is a decent starting effort, maybe 25% of a full search.

[Max0526]

Originally Posted by EdH

This is odd to me. Unless someone can see something I don't, the two separate machines running two separate polys (one each), came back with identical results:

n: 5010968787585504607949192210942377079379285178590004729749207487507787040684433640392691082409304410877720888569557186261540033154512666518900413521876524079689418720554031235001
Y0: -28632061087287122004388923355407648
Y1: 271486670024325210304109
c0: 16169846341318139364012308029717208260097
c1: 12751430081170197232277151268956955
c2: 712058615715448803602419384
c3: -489803879032484011081
c4: 5587786845045
c5: 1302000
skew: 7924630.129
# lognorm 52.90, E 47.61, alpha -5.29 (proj -1.80), 5 real roots
# MurphyE(Bf=1.000e+07,Bg=5.000e+06,area=1.000e+16)=1.239e-13
...

Nothing odd here, you were running CADO, not msieve. It is completely normal, CADO is more deterministic, msieve is more probabilistic. :-)
There were also cases when CADO returned exactly the same poly that was fed into it having gone through the entire spin procedure.

@unconnected: Have you test-sieved this one yet?

[VBCurtis]

Originally Posted by VBCurtis

I've started CADO poly select for 2_1437-.
Parameters:
P=4 million
admin 15k, admax 300k, incr 210
nq = 15625

This is a decent starting effort, maybe 25% of a full search.

Nothing of note, 1.30e-14 score. Continuing from 300k to 2M.