Polynomial Request Thread - Page 215

swellman · 2023-01-27, 17:15

Congrats on the record Ed.

I’ve got a C204 in the same situation - a decent poly scoring 2.67e-15 but it could (and arguably should) be better. If you’re interested I can post it in this thread. If not I certainly understand.

VBCurtis · 2023-01-27, 17:22

If Sean has time, I am quite curious to see a test-sieve comparison between the original 1.21 poly and the spun 1.26 poly. Since this is going to 15e the LP/mfb will be maxed out anyway, so a straight A/B comparison would be nice.

This find also illustrates a CADO poly search quirk- multiple runs with P changed by a factor of 2 or more can be fruitful on these big searches. Smaller changes than factor-of-2 are not efficient- the two runs would overlap.

swellman · 2023-01-27, 18:08

Quote:

Originally Posted by VBCurtis

If Sean has time, I am quite curious to see a test-sieve comparison between the original 1.21 poly and the spun 1.26 poly. Since this is going to 15e the LP/mfb will be maxed out anyway, so a straight A/B comparison would be nice.

This find also illustrates a CADO poly search quirk- multiple runs with P changed by a factor of 2 or more can be fruitful on these big searches. Smaller changes than factor-of-2 are not efficient- the two runs would overlap.

I will test sieve both over the weekend and post the results in this thread.

Tempted to search again for a better poly for my c204 using 2-4 times P. Of course I was also using incr of 4620 rather than 210…high and wide view vs. low and narrow.

EdH · 2023-01-27, 18:37

Quote:

Originally Posted by swellman

Congrats on the record Ed.

I’ve got a C204 in the same situation - a decent poly scoring 2.67e-15 but it could (and arguably should) be better. If you’re interested I can post it in this thread. If not I certainly understand.

Thanks Sean! Go ahead and post it. I can probably run it for a while this weekend, with the same params and see if anything shows up.

swellman · 2023-01-27, 19:49

Quote:

Originally Posted by EdH

Thanks Sean! Go ahead and post it. I can probably run it for a while this weekend, with the same params and see if anything shows up.

C204_147_118 of XYYXF project. My old copy of msieve wants

Code:

expecting poly E from 3.01e-015 to > 3.46e-015

Many weeks of work could only produce a score 88% of this suggested minimum:

Code:

n: 147637954708760577096870566760492577451833118080988439795227165380585466874091608982638794510612975492723170346995368542313930927300923575443335189867125386500916347070672505721942719135313981432615037101
skew: 96927420.776
c0: -3259484283277082819463338965242727394074127124000
c1: -71192934804348078973993341348184817742210
c2: 1393634250179898627313984196395563
c3: 441885881191783807778099
c4: -181100764607727392
c5: 232256640
Y0: -1049185025778492841111809326185936473007
Y1: 1676730684127246452108881
# MurphyE (Bf=8.590e+09,Bg=4.295e+09,area=2.684e+16) = 4.428e-09
# skew 96927420.78, size 5.076e-020, alpha -8.652, combined = 2.669e-015 rroots = 3
#
# cownoise suggests a skew of 136635088.10925 to generate a score of 2.68414524e-15, which I verified via msieve
# skew 136635088.11, size 5.076e-020, alpha -8.652, combined = 2.684e-015 rroots = 3

This poly was found with CADO using the following parameters with the exception of the admin, admax values (which are from my last run) using 16 threads:

Code:

tasks.polyselect.degree = 5

tasks.polyselect.P = 6000000
tasks.polyselect.admin = 2.2e8
tasks.polyselect.admax = 3e8
tasks.polyselect.adrange = 36960
tasks.polyselect.incr = 4620
tasks.polyselect.nq = 15625
tasks.polyselect.nrkeep = 250
tasks.polyselect.ropteffort = 100
tasks.polyselect.sopteffort = 60

Any help or advice gladly accepted.

EdH · 2023-01-29, 03:16

Even after a spin, the best I came up with was 2.52216-15

swellman · 2023-01-29, 03:53

Quote:

Originally Posted by EdH

Even after a spin, the best I came up with was 2.52216-15

Thank you for the spin attempt Ed.

I’ll go back and run another search with revised parameters, primarily incr=210 and P=12M over smaller ranges, e.g. 5M at a time. Maybe I’ll get lucky.

swellman · 2023-01-29, 13:21

Quote:

Originally Posted by VBCurtis

If Sean has time, I am quite curious to see a test-sieve comparison between the original 1.21 poly and the spun 1.26 poly. Since this is going to 15e the LP/mfb will be maxed out anyway, so a straight A/B comparison would be nice.

Results of test seiving for 11+2,289 in the original form (post 2346 above), Ed's first polynomial from post 2349, and finally the spun version from post 2352 (listed below):

Code:

n: 215595066602352118400883082122467079428382835673331189761947112870819155814524658384805320024034304028149189679135083937600896018627033913691610627428059801367594230957982949927522460049055204009
skew: 101228323.627
type: gnfs
lss: 0
c0: 9461155558966299757637585048820949835268210520
c1: -918248262809785119232878863330914017095
c2: -2508004167946129939408265240786
c3: 203361258765417266916623
c4: 302571303235858
c5: -2494800
Y0: -44414703145539847060662740243179435782
Y1: 623758734867750157269763
# lognorm 59.98, E 52.41, alpha -7.57 (proj -2.18), 5 real roots
# MurphyE(Bf=1.000e+07,Bg=5.000e+06,area=1.000e+16)=1.259e-14
# cownoise values: 131586929.62876      1.26494963e-14
rlim: 266000000
alim: 134000000
lpbr: 33
lpba: 33
mfbr: 66
mfba: 96
rlambda: 2.45
alambda: 3.65

Please note the same parameters were used in all three cases, and a total of 955M raw relations were targeted. I used the skew value produced by CADO-NFS, not the suggested value from cownoise.

Results of test sieving on the algebraic side with Q in blocks of 1000:

Code:

          1.01E-14         1.21E-14         1.26E-14
MQ       Norm_yield       Norm_yield       Norm_yield
25          1971             2261             2254
50          2487             2687             2717
75          2576             2785             2912
100         2473             2653             2824
150         2265             2544             2577
200         2086             2329             2399
250         2008             2219             2168
300         1822             2065             2065
350         1699             1898             1871
400         1564             1742             1869
450         1581             1822             1832
500         1463             1705             1736
530         1464               -                -

Q range   25-515M           25-455M          25-450M

One surprising observation was the number of Spec_q in a given q-interval varied wildly between the last two polynomials. I don't see this during multiple test sieving runs on the same number but most of those are on the rational side. FWIW.

Code:

         1.21E-14        1.26E-14
MQ       # Spec_q        # Spec_q
25          80              61
50          53              60
75          54              66
100         58              55
150         71              57
200         59              56
250         54              55
300         50              51
350         48              45
400         51              47
450         53              32
500         60              57

I guess it all comes out in the wash…

charybdis · 2023-01-29, 16:10

Quote:

Originally Posted by swellman

One surprising observation was the number of Spec_q in a given q-interval varied wildly between the last two polynomials. I don't see this during multiple test sieving runs on the same number but most of those are on the rational side. FWIW.

On the rational side the polynomial is linear so it has exactly one root modulo each prime. Result: one special-q per prime, independent of polynomial.

On the algebraic side the polynomial is not linear. Here it's degree 5, so the number of roots modulo a given prime varies from 0 to 5, though the mean is still 1. Naturally this leads to variation in the number of special-q, especially over a range as small as 1k. This isn't an issue because you're normalizing the yield.

swellman · 2023-01-29, 16:19

Quote:

Originally Posted by charybdis

On the rational side the polynomial is linear so it has exactly one root modulo each prime. Result: one special-q per prime, independent of polynomial.

On the algebraic side the polynomial is not linear. Here it's degree 5, so the number of roots modulo a given prime varies from 0 to 5, though the mean is still 1. Naturally this leads to variation in the number of special-q, especially over a range as small as 1k. This isn't an issue because you're normalizing the yield.

Yes, it felt a bit like I was declaring that water is wet but it just surprised me. I’ve test sieved many many polys, with a fraction on the -a side, but just never observed this much noise in the number of spec_q. But as you say, it all gets normalized in the end.

VBCurtis · 2023-01-29, 16:47

Thanks, Sean!
I'm really happy to see that yield is up on the 'spun' poly; I had doubts that spin of 190+ digit jobs was doing much other than removing CADO's optimization for an actual sieve area in favor of optimizing for Murphy's sieve area.
This is a nice bit of evidence that spin works. :)

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2023-01-27, 17:15	#2355
swellman Jun 2012 3,907 Posts	Congrats on the record Ed. I’ve got a C204 in the same situation - a decent poly scoring 2.67e-15 but it could (and arguably should) be better. If you’re interested I can post it in this thread. If not I certainly understand.

2023-01-27, 17:22	#2356
VBCurtis "Curtis" Feb 2005 Riverside, CA 13131₈ Posts	If Sean has time, I am quite curious to see a test-sieve comparison between the original 1.21 poly and the spun 1.26 poly. Since this is going to 15e the LP/mfb will be maxed out anyway, so a straight A/B comparison would be nice. This find also illustrates a CADO poly search quirk- multiple runs with P changed by a factor of 2 or more can be fruitful on these big searches. Smaller changes than factor-of-2 are not efficient- the two runs would overlap.

2023-01-29, 03:16	#2360
EdH "Ed Hall" Dec 2009 Adirondack Mtns 2×2,707 Posts	Even after a spin, the best I came up with was 2.52216-15

2023-01-29, 16:47	#2365
VBCurtis "Curtis" Feb 2005 Riverside, CA 1011001011001₂ Posts	Thanks, Sean! I'm really happy to see that yield is up on the 'spun' poly; I had doubts that spin of 190+ digit jobs was doing much other than removing CADO's optimization for an actual sieve area in favor of optimizing for Murphy's sieve area. This is a nice bit of evidence that spin works. :)