Poly select and CADO sieving for 2,1165+ C217 - Page 4

swellman · 2020-01-20, 22:39

Latest CADO deg 5 search complete, nothing worth reporting (2-handle).

I’m done with CADO deg 5 for awhile. Still looking with msieve-GPU (quintic) however.

swellman · 2020-01-30, 09:07

I got more mediocrity:

Code:

n: 3213773553731676734673029767649076184026081109505643819433123522398392216242493939130914684819990019996494667995485530318906995221039607546449005638410444687839629323036119079997039490112821634482150496640217083568211
skew: 2058663.979
c0: -7227529639082336742982103470079671384153944555
c1: 6164846704258636790237816162225501345606
c2: 24129259369683291720655314363854474
c3: -19182308707757823090942526634
c4: -6301474710764360046959
c5: 561347624034756
c6: -52889760
Y0: -90713561941969834349832662159935024
Y1: 162111780315595201754399887
# MurphyE (Bf=3.436e+10,Bg=1.718e+10,area=8.590e+17) = 1.885e-09
# f(x) = -52889760*x^6+561347624034756*x^5-6301474710764360046959*x^4-19182308707757823090942526634*x^3+24129259369683291720655314363854474*x^2+6164846704258636790237816162225501345606*x-7227529639082336742982103470079671384153944555
# g(x) = 162111780315595201754399887*x-90713561941969834349832662159935024

Cownoise says skew = 2312291.175 gives a score of 4.4625e-16. Not even close to previous top sextic(s).

I am done with CADO searches of any degree for this C217. However I am still plugging away with msieve-GPU searching for a quintic.

swellman · 2020-02-01, 15:51

Quote:

Originally Posted by swellman

Latest CADO deg 5 search complete, nothing worth reporting (2-handle).

I’m done with CADO deg 5 for awhile. Still looking with msieve-GPU (quintic) however.

My GPU using msieve finished its search space today with only a 2-handle reported. I’m done with any further searching for this C217 poly.

Gimarel · 2020-02-02, 09:30

Degree 6 Poly:

Code:

# norm 1.539652e-15 alpha -10.773710 e 6.242975e-16 rroots 4
skew: 19200731.16
c0: 6563328381431671105476687730958294548638654650310
c1: -1918762361267264992524060905783378957147557
c2: -174150593910087798813490057246969159
c3: 13731686969791369412592238867
c4: 578977586331285342649
c5: -23575687256670
c6: 307800
Y0: -261092067112483547589168893048831124
Y1: 38337191767287578050825267

A short testsieving indicates that this poly is a tiny bit better than the previous 6.4e-16 poly.

I have two degree 5 poly for the reference:

Code:

# norm 2.656725e-21 alpha -7.428886 e 3.562884e-16 rroots 3
skew: 33805777.34
c0: -186407826716370335113862643897359103893651875218
c1: 114383776405350799342371085242910198064315
c2: -19606741164333889808309757587619788
c3: 1045588221180880211982927089
c4: 19611168098126871042
c5: 20020160160
Y0: -200131543180127953608923271705080948407984
Y1: 2416652314481504137021

# norm 2.433873e-21 alpha -9.305626 e 3.467306e-16 rroots 3
skew: 1648467371.17
c0: 152846678216810291989513529754965636568937234900682525
c1: -670527287056758688994113376441626943037338110
c2: -2257668140393388020553277621574749709
c3: 130710515042535741225910378
c4: 225363295565144052
c5: 103423320
Y0: -499435443249227062358799483739191334109094
Y1: 2620519854036764841503

The first degree 5 poly sieves about 20% worse than the degree 6 poly. The second degree 5 poly sieves about equal for q above 1e9 but only about 20% for low q because the skew is too high.

I guess to get a competing degree 5 poly we need one with a score of 4.2e-16. I'm not very optimistic but I haven't given up.

R.D. Silverman · 2020-02-03, 01:21

Quote:

Originally Posted by Gimarel

Degree 6 Poly:

Code:

# norm 1.539652e-15 alpha -10.773710 e 6.242975e-16 rroots 4
skew: 19200731.16
c0: 6563328381431671105476687730958294548638654650310
c1: -1918762361267264992524060905783378957147557
c2: -174150593910087798813490057246969159
c3: 13731686969791369412592238867
c4: 578977586331285342649
c5: -23575687256670
c6: 307800
Y0: -261092067112483547589168893048831124
Y1: 38337191767287578050825267

A short testsieving indicates that this poly is a tiny bit better than the previous 6.4e-16 poly.

I have two degree 5 poly for the reference:

Code:

# norm 2.656725e-21 alpha -7.428886 e 3.562884e-16 rroots 3
skew: 33805777.34
c0: -186407826716370335113862643897359103893651875218
c1: 114383776405350799342371085242910198064315
c2: -19606741164333889808309757587619788
c3: 1045588221180880211982927089
c4: 19611168098126871042
c5: 20020160160
Y0: -200131543180127953608923271705080948407984
Y1: 2416652314481504137021

# norm 2.433873e-21 alpha -9.305626 e 3.467306e-16 rroots 3
skew: 1648467371.17
c0: 152846678216810291989513529754965636568937234900682525
c1: -670527287056758688994113376441626943037338110
c2: -2257668140393388020553277621574749709
c3: 130710515042535741225910378
c4: 225363295565144052
c5: 103423320
Y0: -499435443249227062358799483739191334109094
Y1: 2620519854036764841503

The first degree 5 poly sieves about 20% worse than the degree 6 poly. The second degree 5 poly sieves about equal for q above 1e9 but only about 20% for low q because the skew is too high.

I guess to get a competing degree 5 poly we need one with a score of 4.2e-16. I'm not very optimistic but I haven't given up.

Fundamental question: Does the forum have a polynomial that is good enough to hand
off to Greg?

NFS@Home is running 2,2158L. I estimate 6 weeks to sieve. He will need the
polynomial after it finishes.

VBCurtis · 2020-02-03, 04:39

Yes, we have a couple that score well enough to be considered both records for size 217, and that fit the trendline for 210+ digits / degree 6 polynomials.

Surely someone will find time to test-sieve to confirm which poly is best- Gimarel suggests his new one beats mine, which is great news!

swellman · 2020-02-03, 22:21

Quote:

Originally Posted by VBCurtis

Yes, we have a couple that score well enough to be considered both records for size 217, and that fit the trendline for 210+ digits / degree 6 polynomials.

Surely someone will find time to test-sieve to confirm which poly is best- Gimarel suggests his new one beats mine, which is great news!

I can run some test sieving later this week and identify the best deg 5 and 6 polynomial found to date.

swellman · 2020-02-06, 19:03

Top 3 scores for degree 6 polys:

Code:

# norm 1.602538e-15 alpha -10.543517 e 6.454054e-16 rroots 6
skew: 3226967.46
c0: -2543005241608251659326321959460452765214183842
c1: -33139987534593547344167381165622666435255
c2: 15215551779833751980190681203957330
c3: 17257164061453212524534319695
c4: -1977227853181703834928
c5: -958120310818440
c6: 39916800
Y0: -110056071714162569817319860596637820
Y1: 14771789483157557668102843


# cownoise calculated score of 6.25337175e-16
skew: 2382635.076
c0: 3987095627700723668556412616355906815127705992
c1: 10621479627429548899812810235604051573030
c2: -4682349569391313556729607478081235
c3: -18433207794474459950952563135
c4: 1015293418294354295928
c5: 1005061270114440
c6: -39916800
Y0: -110058966911042321282835020413351605
Y1: 14771789483157557668102843
# MurphyE (Bf=3.436e+10,Bg=1.718e+10,area=2.147e+16) = 1.201e-08


# norm 1.539652e-15 alpha -10.773710 e 6.242975e-16 rroots 4
skew: 19200731.16
c0: 6563328381431671105476687730958294548638654650310
c1: -1918762361267264992524060905783378957147557
c2: -174150593910087798813490057246969159
c3: 13731686969791369412592238867
c4: 578977586331285342649
c5: -23575687256670
c6: 307800
Y0: -261092067112483547589168893048831124
Y1: 38337191767287578050825267

Top 2 scores for degree 5 polys:

Code:

# norm 2.656725e-21 alpha -7.428886 e 3.562884e-16 rroots 3
skew: 33805777.34
c0: -186407826716370335113862643897359103893651875218
c1: 114383776405350799342371085242910198064315
c2: -19606741164333889808309757587619788
c3: 1045588221180880211982927089
c4: 19611168098126871042
c5: 20020160160
Y0: -200131543180127953608923271705080948407984
Y1: 2416652314481504137021


# cownoise calculated score of 3.441e-16
skew: 81925937.712
c0: 20979117737896229889501593134036124581546875899439
c1: 702888888638716632053630701142158258021494
c2: 4805942957212842715569169595729246
c3: -1015952315801263566432172936
c4: -1641253174806907117
c5: 970539570
Y0: -319154102222244908033626629552413265381850
Y1: 56066781401775656648141249
# MurphyE (Bf=3.436e+10,Bg=1.718e+10,area=8.590e+17) = 2.372e-09
# f(x) = 970539570*x^5-1641253174806907117*x^4-1015952315801263566432172936*x^3+4805942957212842715569169595729246*x^2+702888888638716632053630701142158258021494*x+20979117737896229889501593134036124581546875899439
# g(x) = 56066781401775656648141249*x-319154102222244908033626629552413265381850

The rest are too low scoring. Listing these here in the hope that Max can spin some/all up a bit.

Once Max does his thing (if possible), I will test sieve each on 16e for 10,000 Q @40M, @150M and @~~300M~~. Correction 400M

Max0526 · 2020-02-07, 23:23

@swellman
Thank you for the PM.
I saw the 5 polys. I'll do my best during this weekend and answer with my findings here.

Gimarel · 2020-02-08, 07:41

Quote:

Originally Posted by swellman

Top 3 scores for degree 6 polys:

Note that this poly

Code:

 # norm 1.602538e-15 alpha -10.543517 e 6.454054e-16 rroots 6

is an msieve optimization of this poly:

Code:

 # cownoise calculated score of 6.25337175e-16

One more degree 6 poly. I didn't testsieve this poly.

Code:

# norm 1.532885e-15 alpha -10.663919 e 6.167586e-16 rroots 6
skew: 13169474.90
c0: 1023735201309774246420532958336660120924961565920
c1: 995951334583249051832847919997394867745920
c2: 228409353245738642065033416449151622
c3: -7991582155794456227507263689
c4: -2040419130460960418821
c5: 61122488216070
c6: 693000
Y0: -227484134920273250744569883728074583
Y1: 10110547595475849804503267

Max0526 · 2020-02-08, 13:22

Quote:

Originally Posted by swellman

Top 2 scores for degree 5 polys:

Code:

# norm 2.656725e-21 alpha -7.428886 e 3.562884e-16 rroots 3
skew: 33805777.34
c0: -186407826716370335113862643897359103893651875218
c1: 114383776405350799342371085242910198064315
c2: -19606741164333889808309757587619788
c3: 1045588221180880211982927089
c4: 19611168098126871042
c5: 20020160160
Y0: -200131543180127953608923271705080948407984
Y1: 2416652314481504137021

Just for reference, there is one here that is a bit lower (but still higher than the next top scoring degree 5):

Code:

Y0: -200131543180153229931310466087596002561814
Y1: 2416652314481504137021
c0: -4491829208299024732947205309178495582822026700868
c1: 779116650391269131588854564129131560499095
c2: -39771713110588658172491572498053398
c3: 247018503097833034497096449
c4: 18564190799375487042
c5: 20020160160
skew: 42238597.02444
# size 2.197e-21, alpha -7.429, combined = 3.545e-16 rroots = 3

2020-02-07, 23:23	#42
Max0526 "Max" Jun 2016 Toronto 23×31 Posts	C217 polys @swellman Thank you for the PM. I saw the 5 polys. I'll do my best during this weekend and answer with my findings here.

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2020-01-20, 22:39	#34
swellman Jun 2012 101101111111₂ Posts	Latest CADO deg 5 search complete, nothing worth reporting (2-handle). I’m done with CADO deg 5 for awhile. Still looking with msieve-GPU (quintic) however.

2020-02-03, 04:39	#39
VBCurtis "Curtis" Feb 2005 Riverside, CA 2⁴·17² Posts	Yes, we have a couple that score well enough to be considered both records for size 217, and that fit the trendline for 210+ digits / degree 6 polynomials. Surely someone will find time to test-sieve to confirm which poly is best- Gimarel suggests his new one beats mine, which is great news!