Polynomial Request Thread

[Max0526]

Originally Posted by VBCurtis

swellman and I like a challenge, so we're going to factor 138139^123+123^139138. 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

n: 32030731016440682777065354721302752319396528561887718275010943791422401733138770874875013988992282966916694379386222588227067753509923096299768661077024692164623187468602947896220375896898149402189690061819

This C206 is a cofactor of 139^123+123^139: http://factordb.com/index.php?id=1100000000032300702

[Max0526]

Kurt Beschorner's team (http://kurtbeschorner.de/) is ready to tackle the smallest repunit cofactor, R1620L / 10^810+1 (C185): http://factordb.com/index.php?id=1100000000080356921

n: 21431956757675468974876300755804900832277300719777308299609301048389700236714216988820459065467670651445681992662548793310029766116893035870982334672674080173615607829147502498184662701

WayBack Machine lists this number on Makoto Kamada's page four years ago (to the day): https://web.archive.org/web/20150330...m/nrr/repunit/
With the team's resources this C185 can be split fairly fast by GNFS.
We ask you to please contribute some cycles to our poly search.
I am starting CADO on 0-1M today.
Please post any poly with E >= 3.5e-14, I'll try my best to spin it.
A year old record is held by VBCurtis: E = 4.146e-14: https://mersenneforum.org/showpost.p...&postcount=134, https://mersenneforum.org/showpost.p...&postcount=131

[firejuggler]

then i'll get 1M to 2M

[Max0526]

Records for
C186 -- 4.010e-14 -- https://mersenneforum.org/showpost.p...&postcount=130
C185 -- 4.146e-14 -- https://mersenneforum.org/showpost.p...&postcount=131
C184 -- 5.568e-14 -- https://mersenneforum.org/showpost.p...&postcount=148
My dream goal would be E = 4.725e-14.
With all the luck, I can spin it there starting from E = 4e-14.

[Max0526]

Y0: -593175712609252133119762635675564154
Y1: 283859127488700701119
c0: 79550633174452398067887636627979632530551130
c1: 1778187528400431236556101254436970473
c2: -2136174372192787879877681398775
c3: 18237717523482307292206
c4: 3443314402690944
c5: 3502080
skew: 27283554.02
# size 3.467e-18, alpha -7.863, combined = 3.682e-14 rroots = 5

[RichD]

I'll start at 4M.
An early flare.

N: 21431956757675468974876300755804900832277300719777308299609301048389700236714216988820459065467670651445681992662548793310029766116893035870982334672674080173615607829147502498184662701
# expecting poly E from 4.19e-14 to > 4.81e-14
R0: -350598613896110727506748524784785867
R1: 1151497920648681839
A0: 2373212050810275198687137585303473937376684
A1: 3275547526683773941017960768058346592
A2: 409743365967645834442712538309
A3: -26473835725472363986472
A4: -436117661119538
A5: 4045860
skew 27709855.41, size 4.393e-18, alpha -6.681, combined = 4.280e-14 rroots = 5

[Max0526]

RichD's early flare is a new record!

[Max0526]

Originally Posted by RichD

I'll start at 4M.
An early flare.

N: 21431956757675468974876300755804900832277300719777308299609301048389700236714216988820459065467670651445681992662548793310029766116893035870982334672674080173615607829147502498184662701
# expecting poly E from 4.19e-14 to > 4.81e-14
R0: -350598613896110727506748524784785867
R1: 1151497920648681839
A0: 2373212050810275198687137585303473937376684
A1: 3275547526683773941017960768058346592
A2: 409743365967645834442712538309
A3: -26473835725472363986472
A4: -436117661119538
A5: 4045860
skew 27709855.41, size 4.393e-18, alpha -6.681, combined = 4.280e-14 rroots = 5

CADO already got 4.4 out of this RichD's poly!

[firejuggler]

is it even worthy to try, now?

[VBCurtis]

Originally Posted by firejuggler

is it even worthy to try, now?

A 4.6 fits the trendline well enough that I'd quit if I were searching; a 4.4 is in that "good enough to sieve, but we'd like better" range IMO.

Edit: leading digit 2 means a trend-fitting record is rather unlikely; I just thought to check that, so maybe 4.5 is a reasonable target and Max's spin might get you there.

[Max0526]

Originally Posted by RichD

I'll start at 4M.
An early flare.

N: 21431956757675468974876300755804900832277300719777308299609301048389700236714216988820459065467670651445681992662548793310029766116893035870982334672674080173615607829147502498184662701
# expecting poly E from 4.19e-14 to > 4.81e-14
R0: -350598613896110727506748524784785867
R1: 1151497920648681839
A0: 2373212050810275198687137585303473937376684
A1: 3275547526683773941017960768058346592
A2: 409743365967645834442712538309
A3: -26473835725472363986472
A4: -436117661119538
A5: 4045860
skew 27709855.41, size 4.393e-18, alpha -6.681, combined = 4.280e-14 rroots = 5

After spin:

Y0: -350598613903509620972478518155870256
Y1: 1151497920648681839
c0: -170298280842407947441885762065122759920574925
c1: 11005145721010187685436156290531598455
c2: 801294931544507511591503591142
c3: -13594434303837748041320
c4: -566100037033838
c5: 4045860
skew: 40806382.44
# size 4.626e-18, alpha -7.081, combined = 4.428e-14 rroots = 5