Reserved for MF - Sequence 276 - Page 10

VBCurtis · 2020-11-26, 03:52

Select params: Admin 1e4, admax 1e6, incr 420, nq 7776.
Best find:

Code:

skew: 631979.278
c0: 221680841467084554375313043201589174040123200
c1: 901626333096189223856973821582271143206
c2: -4177775485275183261925822500403331
c3: -3628307161884760901626257457
c4: 17768364794680671699524
c5: 1604264371733172
c6: 56568960
Y0: -25234491453876474941390497951904367
Y1: 21605860128541321690123
# MurphyE (Bf=1.718e+10,Bg=1.718e+10,area=2.577e+17) = 2.313e-09

Cownoise provides: skew 1139176.04087 score 8.19198927e-16
Next I'll run admin 1e6 admax 5e6, same other params. That should take 2 days or so.
1.5e-15 is a decent poly; if we hit 2e-15 on degree 6 I'd stop the search.

EdH · 2020-11-26, 15:44

I ran a VERY brief search working with some new scripts here, from 1e6-1.1e6, with everything else default:

Code:

n: 1398516542119091547927880887727114963659389509804105922692120268647401334715710534035357328326678677296622476655524803463753551464210096969080964891534065442657109752753516921412646600842893476177
skew: 545830603.975
c0: -14971629648878549524808087247752464364965298518000
c1: -14761544728683333612065798704663255596204
c2: 1287342178886895395085353453150732
c3: -140985462445644677795529
c4: -842136846439078
c5: 1022580
Y0: -67176123977078727734001177678602812089
Y1: 19604334531133990141482371
# MurphyE (Bf=8.590e+09,Bg=4.295e+09,area=2.684e+16) = 8.143e-09
# f(x) = 1022580*x^5-842136846439078*x^4-140985462445644677795529*x^3+1287342178886895395085353453150732*x^2-14761544728683333612065798704663255596204*x-14971629648878549524808087247752464364965298518000
# g(x) = 19604334531133990141482371*x-67176123977078727734001177678602812089

cownoise response:

Code:

629212237.66888 7.35605497e-15

VBCurtis · 2020-11-26, 16:48

Something doesn't make sense there- 7e-15 would be a record score for a C199, 14 digits smaller. I think you have the wrong input number!
Try:

Code:

n: 105846620118997527795673923816494096564538879551655755948941841181964527982935974672375053674066636955526325748344171237200759216056332103525354574858042635016393534861038293333116405407677018242280598840418822711

EdH · 2020-11-26, 17:31

Quote:

Originally Posted by VBCurtis

Something doesn't make sense there- 7e-15 would be a record score for a C199, 14 digits smaller. I think you have the wrong input number!
Try:

Code:

n: 105846620118997527795673923816494096564538879551655755948941841181964527982935974672375053674066636955526325748344171237200759216056332103525354574858042635016393534861038293333116405407677018242280598840418822711

Oops! My script preparation was poor!

I don't think I'll try again right now. I'm going to hang my head and sneak away and hide for a while. . . (So far, today has shown a consistency of events that has been less than encouraging.)

Gimarel · 2020-11-27, 08:21

I think, that you have to be very lucky to reach 1.5e-15.
My two best polys so far (msieve GPU):

Code:

# norm 2.760058e-15 alpha -9.741804 e 9.089e-16 rroots 6
skew: 5514169.01
c0: -4876614572131949342216622679934518737712151744
c1: 1236437678859007532084165367703778552216
c2: 8860645366164470554474235991463436
c3: 1224313061012770020317249742
c4: -1623375565991248247517
c5: -3913813493348
c6: 13860
Y0: -66186159218259333947073228354928683
Y1: 159873288130101231999311

# norm 2.683070e-15 alpha -10.854522 e 9.088e-16 rroots 4
skew: 27730596.42
c0: 1155157890746619338478428016822594927819557893488
c1: -1099716488327948240738249749673850866379372
c2: 298865657895349450713496106011396564
c3: 2723566691875907416869763557
c4: -1091912115304923826567
c5: -5149699096440
c6: 30240
Y0: -66182278006915508431673355332592277
Y1: 128624999052151775688551

swellman · 2020-11-27, 13:25

My interpolation over the best deg 6 polys says 9.2e-16 is the best expected value for a C213. And the trend line includes the poly for C212 from RSA-704: presumably they threw a lot of time and hardware towards that effort, so its e-score is likely above the trend line even 8 years later.

The fact that you guys are finding polynomials with such good e-scores after only a couple of days of searching is very encouraging.

VBCurtis · 2020-11-27, 15:46

1e6-5e6 on CADO deg 6:

Code:

n: 105846620118997527795673923816494096564538879551655755948941841181964527982935974672375053674066636955526325>
skew: 1456435.368
c0: -1170995460057999016831857396880484893783705248
c1: 1985420792625283081838789754308133374604
c2: 5676994570714226964059196219040304
c3: -5624572569087135303119321985
c4: -3421207947416187525629
c5: 872904281150538
c6: 79115400
Y0: -19569229193985586683043682156063095
Y1: 910877534232699487771241
# MurphyE (Bf=1.718e+10,Bg=1.718e+10,area=2.577e+17) = 2.428e-09

Cownoise gives me a blank screen when I enter this one, so I don't know msieve score. CADO scores it nearly 5% above my previous poly, suggesting an msieve score in the high 8's or 9.0 e-16.

I do think we need to be very lucky to hit 1.5e-15; I also think a job that will sieve for ~120 core-years calls for quite a lot of poly select!

Running 5-10M next.

chris2be8 · 2020-11-27, 16:48

The first line of the .poly posted above is incomplete, it ends 636955526325> which would probably upset cownoise.

Replacing that with the number in post 102 I get:

Code:

chris@rigel:~/bin$ vi t.poly
chris@rigel:~/bin$ rate_poly.pl t.poly
This is the tester script, it just checks the poly without sieving any relations
-> Starting Fri Nov 27 16:43:02 2020
-> Working with NAME=t...
-> Selected default factorization parameters for degree 6 gnfs 213 digit level.
-> Selected lattice siever: /home/chris/lasieve4_64/gnfs-lasieve4I16e
-> Using rlim=596600000, alim=596600000, lpbr=32, lpba=32, mfbr=64, mfba=64, rlambda=2.6, alambda=2.6, qintsize 100000
-> Skew 1456435.368 was provided, the default skew would be 1566927.96151543
aa is 65536, bb is 32768, degree is 6, c6 is 79115400, c0 is -1170995460057999016831857396880484893783705248, Y1 is 910877534232699487771241, Y0 is -19569229193985586683043682156063095
sqr_lim is 24425.396619093, sqrt(skew) is 1206.82864069428, aa is now 1931822248770.84, bb is now 663202.189131004
c0 is -1170995460057999016831857396880484893783705248, adding -9.96393573623812e+79
c1 is 1985420792625283081838789754308133374604, adding 4.92095603244425e+80
c2 is 5676994570714226964059196219040304, adding 4.09861014096906e+81
c3 is -5624572569087135303119321985, adding -1.18284780504208e+82
c4 is -3421207947416187525629, adding -2.09575267173796e+82
c5 is 872904281150538, adding 1.55757293532401e+82
c6 is 79115400, adding 4.11210323655082e+81
-> Algebraic norm is 8.60710579115833e+81. Rational norm is 1.29801152945441e+40.
-> Algebraic difficulty is about 81.9349. Rational difficulty is about 40.1133.
msieve rating: skew 1456435.37, size 2.109e-15, alpha -9.705, combined = 8.666e-16 rroots = 6

This is a script of mine to check .polys and get the msieve rating.

Chris

RichD · 2020-11-27, 17:06

I ran it through Msieve and this is what it shows.

Code:

commencing number field sieve (213-digit input)
R0: -19569229193985586683043682156063095
R1: 910877534232699487771241
A0: -1170995460057999016831857396880484893783705248
A1: 1985420792625283081838789754308133374604
A2: 5676994570714226964059196219040304
A3: -5624572569087135303119321985
A4: -3421207947416187525629
A5: 872904281150538
A6: 79115400
skew 1456435.37, size 2.109e-15, alpha -9.705, combined = 8.666e-16 rroots = 6

VBCurtis · 2020-11-27, 17:11

Quote:

Originally Posted by chris2be8

The first line of the .poly posted above is incomplete, it ends 636955526325> which would probably upset cownoise.

Chris

cownoise doesn't take the input number, so that wasn't the problem. Thanks for scoring it for me!

EdH · 2020-11-27, 18:02

Am I possibly back on the right track?:

Code:

n: 105846620118997527795673923816494096564538879551655755948941841181964527982935974672375053674066636955526325748344171237200759216056332103525354574858042635016393534861038293333116405407677018242280598840418822711
skew: 2185756.75
c0: 1011662942913749734451703761220924989470389600
c1: 3368550033557676300983013286430685948160
c2: -1351529129369905219806888867723006
c3: -3469322398149168263657031635
c4: 189765598430432507867
c5: 22275776007506
c6: 11999880
Y0: -16134479797147154048440211858006311
Y1: 5640686983714034914241
# MurphyE (Bf=3.436e+10,Bg=1.718e+10,area=1.476e+17) = 6.205e-09
# f(x) = 11999880*x^6+22275776007506*x^5+189765598430432507867*x^4-3469322398149168263657031635*x^3-1351529129369905219806888867723006*x^2+3368550033557676300983013286430685948160*x+1011662942913749734451703761220924989470389600
# g(x) = 5640686983714034914241*x-16134479797147154048440211858006311

cownoise:

Code:

2569917.66851 8.96484506e-16

Script parameters:

Code:

P="tasks.polyselect.P=8000000"
min="tasks.polyselect.admin=5700000"
max="tasks.polyselect.admax=6000000"
incr="tasks.polyselect.incr=60"
range="tasks.polyselect.adrange=1000"
se="tasks.polyselect.sopteffort=10"

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2020-11-26, 03:52	#100
VBCurtis "Curtis" Feb 2005 Riverside, CA 1001000000010₂ Posts	Select params: Admin 1e4, admax 1e6, incr 420, nq 7776. Best find: Code: skew: 631979.278 c0: 221680841467084554375313043201589174040123200 c1: 901626333096189223856973821582271143206 c2: -4177775485275183261925822500403331 c3: -3628307161884760901626257457 c4: 17768364794680671699524 c5: 1604264371733172 c6: 56568960 Y0: -25234491453876474941390497951904367 Y1: 21605860128541321690123 # MurphyE (Bf=1.718e+10,Bg=1.718e+10,area=2.577e+17) = 2.313e-09 Cownoise provides: skew 1139176.04087 score 8.19198927e-16 Next I'll run admin 1e6 admax 5e6, same other params. That should take 2 days or so. 1.5e-15 is a decent poly; if we hit 2e-15 on degree 6 I'd stop the search.

2020-11-26, 16:48	#102
VBCurtis "Curtis" Feb 2005 Riverside, CA 11002₈ Posts	Something doesn't make sense there- 7e-15 would be a record score for a C199, 14 digits smaller. I think you have the wrong input number! Try: Code: n: 105846620118997527795673923816494096564538879551655755948941841181964527982935974672375053674066636955526325748344171237200759216056332103525354574858042635016393534861038293333116405407677018242280598840418822711

2020-11-27, 13:25	#105
swellman Jun 2012 3³·109 Posts	My interpolation over the best deg 6 polys says 9.2e-16 is the best expected value for a C213. And the trend line includes the poly for C212 from RSA-704: presumably they threw a lot of time and hardware towards that effort, so its e-score is likely above the trend line even 8 years later. The fact that you guys are finding polynomials with such good e-scores after only a couple of days of searching is very encouraging.