mersenneforum.org - Polynomial Request Thread

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Hello, I need a good poly for C178 from 11040:i10112. Here is my best:

[CODE]n: 7892799572500156361411841068876751860118316870434909321288561346733923011110349902199528137633455661337796437514526770626821570367806592979750554768540808484867280448678051526201
# norm 2.260265e-17 alpha -7.530592 e 1.040e-13 rroots 3
skew: 97936058.52
c0: 148292812285264937077050381395797838139409224
c1: 20425177968991700916631128385620281490
c2: -50687467952977089830606679549
c3: -5457542910124349545748
c4: 23749354032668
c5: 170940
Y0: -34109666347903949347580476293688345
Y1: 10527761608994650169
[/CODE]

[QUOTE=unconnected;509119]Hello, I need a good poly for C178 from 11040:i10112. Here is my best:

[CODE]n: 7892799572500156361411841068876751860118316870434909321288561346733923011110349902199528137633455661337796437514526770626821570367806592979750554768540808484867280448678051526201
# norm 2.260265e-17 alpha -7.530592 e 1.040e-13 rroots 3
skew: 97936058.52
c0: 148292812285264937077050381395797838139409224
c1: 20425177968991700916631128385620281490
c2: -50687467952977089830606679549
c3: -5457542910124349545748
c4: 23749354032668
c5: 170940
Y0: -34109666347903949347580476293688345
Y1: 10527761608994650169
[/CODE][/QUOTE]
These two spin-offs are close but lower:[code]Y0: -34109666349145319829943471473715811
Y1: 21055523217989300338
c0: 36470925514554224749946956742891870356916400
c1: 10218451848650952047211242864112113635
c2: -48754927386340552657482856965
c3: -10937441336891442563112
c4: 94594291747472
c5: 1367520
skew: 50588693.31
# size 1.731e-17, alpha -7.993, combined = 9.979e-14 rroots = 3[/code][code]Y0: -34109666349154805343153175653518080
Y1: 31583284826983950507
c0: 5402418087718901155324238613438042612857587
c1: 2270776837818049596578734740303560440
c2: -16246715106395794410527874963
c3: -5468805896514893124428
c4: 70943408556504
c5: 1538460
skew: 33730849.29
# size 1.557e-17, alpha -6.981, combined = 9.361e-14 rroots = 3[/code]

Completed my search. Best I found was awful (1.15e-14). And I am done with this poly search.

[QUOTE=unconnected;509119]Hello, I need a good poly for C178 from 11040:i10112. Here is my best:

[CODE]n: 7892799572500156361411841068876751860118316870434909321288561346733923011110349902199528137633455661337796437514526770626821570367806592979750554768540808484867280448678051526201
# norm 2.260265e-17 alpha -7.530592 e 1.040e-13 rroots 3
skew: 97936058.52
c0: 148292812285264937077050381395797838139409224
c1: 20425177968991700916631128385620281490
c2: -50687467952977089830606679549
c3: -5457542910124349545748
c4: 23749354032668
c5: 170940
Y0: -34109666347903949347580476293688345
Y1: 10527761608994650169
[/CODE][/QUOTE]

Best I found in 1-2M, maybe it can be spun higher?
[CODE]
# norm 2.019027e-17 alpha -7.574254 e 9.488e-14 rroots 5
skew: 30943061.75
c0: 9592092048339354727701393648835835896257480
c1: 1820677362305896000055738689805391116
c2: -287211571023407522438460472978
c3: -21514599853813091805139
c4: 326306440091672
c5: 1335180
Y0: -22611962222760044066251474353394207
Y1: 34899159750771853
[/CODE]

I'm done searching unless you need more.

[QUOTE=swellman;509368]Best I found in 1-2M, maybe it can be spun higher?
[CODE]
# norm 2.019027e-17 alpha -7.574254 e 9.488e-14 rroots 5
skew: 30943061.75
c0: 9592092048339354727701393648835835896257480
c1: 1820677362305896000055738689805391116
c2: -287211571023407522438460472978
c3: -21514599853813091805139
c4: 326306440091672
c5: 1335180
Y0: -22611962222760044066251474353394207
Y1: 34899159750771853
[/CODE]I'm done searching unless you need more.[/QUOTE]
It spins a bit higher:[code]Y0: -22611962222752983198452378690551541
Y1: 69798319501543706
c0: 1243565090731471667505657455336863942756800
c1: 425456924004144725408908048866304520
c2: -150094974258986250472682445482
c3: -21249977422383656324403
c4: 655314243062944
c5: 5340720
skew: 15514895.57
# size 1.670e-17, alpha -7.575, combined = 9.573e-14 rroots = 5[/code]

swellman and I like a challenge, so we're going to factor 138^123+123^138. It's a C206, by GNFS.
frmky has agreed to add this to the 16e queue, provided we manage the matrix ourselves. I think I have MPI running properly on a dual-10-core Ivy Bridge w/64GB, which should be sufficient to handle the matrix.

Anyway, we need a polynomial for
[code]n: 32030731016440682777065354721302752319396528561887718275010943791422401733138770874875013988992282966916694379386222588227067753509923096299768661077024692164623187468602947896220375896898149402189690061819[/code]

We've done a few days of both deg 5 and deg 6 searching. Best deg 6 came from CADO, with msieve score 1.78e-15:
[code]Y0: -1893541435368488534780673122503183
Y1: 320415766494990567576989
c0: 196081352677430156130812951070224441857680
c1: -11485697830982755148530574184804075126
c2: -175035960220343226358329027663289
c3: 369368648513389114143033174
c4: 1531702226937017688853
c5: -875685414083454
c6: -162456840
skew: 367200.539[/code]

Best deg 5 sieves *much* better; score (After passing skew through jcrombie's tool) 1.616e-15. This also came from CADO:
[code]skew: 195909916.41542 #89841894.929
c0: -342734039509470197880200377148639002499532983568
c1: 119447402541993708305502542771878664057074
c2: 1798571475044456627105465017294061
c3: -41362494378488593672270211
c4: -110597773826728986
c5: 1375920
Y0: -15781640997291840620627528117066756157195
Y1: 242995154421821201088071219[/code]

I have no record poly scores for C206; the C207 record is 1.627e-15, while C205 is 2.21e-15 (from aliq276 that still isn't factored). Judging from records, 1.90 is possible and 1.85+ is a reasonable target.

Sean is msieve-searching 9-11M on deg 5; we have covered 0-3M on deg 6 already. I'm searching 25-27M on deg 5.
If anyone wishes to try CADO, I'll share the parameters I used to cover 0-1M deg 6 and 0-100k deg 5.

Thanks to everyone who can throw some cycles at poly searching for this GNFS 206 job. And of course a big thank you in advance to Greg for sieving and to Mike for his kind offer to postprocess. And thanks to Max for his spin alchemy.

No doubt most here are familiar with Jonathan Crombie’s website including the skew optimizer, but for reference it is located [url=http://myfactors.mooo.com]here[/url].

I’m focusing on searching with msieve in degree 5, but there are many directions searchers can take. Have fun!

Insignificantly better one:[code]Y0: -15781646476479500873320706447891777125988
Y1: 242995154421821201088071219
c0: -1676036686598938146239825587550623118136017551050
c1: -19680030737885163992693361794303610557445
c2: 4259014194800901061020630651748268
c3: -31380222287596575297064043
c4: -110752898810670186
c5: 1375920
skew: 200481763.10
# size 2.336e-20, alpha -8.506, combined = 1.617e-15 rroots = 5[/code]

C206 deg 6 (Msieve)

[CODE]# norm 6.662894e-15 alpha -9.134665 e 1.699e-15 rroots 6
skew: 5442451.72
c0: -4167976492353839289329841939164864718615150765
c1: 23842371361320783282270816024329206803570
c2: 6456627008274315343084687234941697
c3: -2185722867108028051159990061
c4: -333002463294833171396
c5: 55204208909859
c6: 2419032
Y0: -1538110509019924623644547756159622
Y1: 37440602880485897
[/CODE]

Maybe it can be spun higher by Max, however the Crombie tool offered little improvement.

Now back to searching deg 5 in 9-11M range with Msieve.

I will try to find something convincing, starting tommorrow, starting at 5M, with deg 5