Poly select and planning for 2,2330M

VBCurtis · 2019-05-20, 20:14

Poly select and ECM have finished for 2330L, so we're on to begin factorization of 2330M:

Code:

201916700580745604776027022665471186255107062245932082076863383752096343903385041484073267281054478199044604641397575671739630499971150912819790916215008125554106571022882316742647109864486081319721103021177161

We don't know who will factor this number, but NFS@home and forum-team-CADO are both reasonable choices; either way, a good poly will help get the number into NFS.

On 2330L, Vebis did extensive CADO searching. He found a deg 6 at 1.94e-15, and deg 5 at 1.76e-15 (both after Max' spin efforts, which even he found lucky). Vebis also found a 1.65e-15 with CADO, which was not significantly changed by spin (1.66 best, I believe). Vebis' efforts were close to 4 core-years of poly select!!! By traditional measures, too much; however, he did deg 6 first and then learned that we expected deg 5 to be better, so repeated his search on deg 5.

msieve-GPU deg 5 produced quite a few hits in the 1.40's, none of which spun into 1.60s so none were test-sieved.

This C210 is roughly 50% harder than the C207 of 2330L. Poly scores around 1e-15 deg 5 before spin are good hits, 1.1e-15 for deg 6. The record score is deg 6, found by the CADO team for RSA210, at 1.49e-15. The CADO folks indicate deg 6 is preferred for this composite size, but experience in msieve is that deg 5 is more likely to produce a better poly.

So, I suggest CADO folks aim at deg 6, msieve-gpu folks at deg 5. Naturally, anyone can do what they like, and any software/degree combo surely can produce the winning polynomial. As always, please post your search range to this thread before you search, to reduce overlapping efforts among contributors.

VBCurtis · 2019-05-22, 22:52

I am poly selecting with CADO: deg 5 admin 10M admax 20M with nq = 15625 and incr = 4620. These are the settings that produced the best pre-spin score from Vebis' work on 2330L.
It'll be a few days.

Dylan14 · 2019-05-23, 13:40

I'll do some polyselect as well on CADO, with the following parameters:

Code:

tasks.polyselect.degree = 5

tasks.polyselect.P = 10000000
tasks.polyselect.admin = 20e6
tasks.polyselect.admax = 25e6
tasks.polyselect.adrange = 4620
tasks.polyselect.incr = 4620
tasks.polyselect.nq = 15625 
tasks.polyselect.nrkeep = 120
tasks.polyselect.sopteffort = 20
tasks.polyselect.ropteffort = 0 #Max can handle the spinning
tasks.wutimeout = 86400 # one day

On second thought, maybe not. The tasks seem to take a long time, and I don’t have that many cores.

VBCurtis · 2019-05-23, 15:17

I believe the "long time" is caused by sopteffort set to 20. If you delete that, you should be OK. I'm running 4-threaded without specifying sopteffort and a 10M range is going to take around 6 days, so your reservation would be around 12-thread-days (I'm using all hyperthreads of an i7, so a non-HT machine would be about half this time).

Also, note that adrange = incr means there is just one c5 value to test in each workunit, but default workers are 2-threaded. If you use adrange = 4 * incr = 18480 the workers will balance better and more fully utilize the threads allocated.

Dylan14 · 2019-05-23, 16:52

Ok, I have removed the sopteffort line and adjusted adrange in my params file and I will carry on with the reservation. I'm running it on a i5-6400 (4c, 4t) which is also running mmff, so I will keep you posted on progress.
By the way, this is the largest number that I have tried to find a poly for.

VBCurtis · 2019-05-23, 21:30

I appreciate your effort to help out, Dylan!

Dylan14 · 2019-05-25, 22:58

Search completed on CADO deg 5, 20M-25M. Here is the best poly I found:

Code:

n: 201916700580745604776027022665471186255107062245932082076863383752096343903385041484073267281054478199044604641397575671739630499971150912819790916215008125554106571022882316742647109864486081319721103021177161
skew: 315989367.585
c0: -8270680653880308830460607153894875173790667310385
c1: 3222328796747943800553552491255403933558589
c2: -381701881608412474793873349117993
c3: -763777506196945863233850109
c4: -111143744685556902
c5: 685460160
Y0: -24977029893574927325366834708458313140408
Y1: 1847059793854092133595999
# MurphyE (Bf=3.436e+10,Bg=1.718e+10,area=5.369e+15) = 2.59e-08
# found by revision 50ad0f1fd
# f(x) = 685460160*x^5-111143744685556902*x^4-763777506196945863233850109*x^3-381701881608412474793873349117993*x^2+3222328796747943800553552491255403933558589*x-8270680653880308830460607153894875173790667310385
 # g(x) = 1847059793854092133595999*x-24977029893574927325366834708458313140408

Now to see if Max can work his magic...

VBCurtis · 2019-05-25, 23:24

cownoise says:
skew 239563346.43219 score 8.00005243e-16

I'll have a poly Tuesday.

Gimarel · 2019-05-27, 13:31

My first poly:

Code:

# norm 1.289220e-20 alpha -8.622866 e 9.745e-16 rroots 5
skew: 333353621.30
c0: -1330621012689673651205516325031368291157533624229440
c1: 2801419174198604069043508544608185474604632
c2: 68749078877640382414219776780695762
c3: -78231304031873583067593517
c4: -859938876210389022
c5: 202161960
Y0: -15845084526885064580819079083140525077823
Y1: 224396622703251576439

swellman · 2019-05-27, 13:39

Quote:

Originally Posted by Gimarel

My first poly:

Code:

# norm 1.289220e-20 alpha -8.622866 e 9.745e-16 rroots 5
skew: 333353621.30
c0: -1330621012689673651205516325031368291157533624229440
c1: 2801419174198604069043508544608185474604632
c2: 68749078877640382414219776780695762
c3: -78231304031873583067593517
c4: -859938876210389022
c5: 202161960
Y0: -15845084526885064580819079083140525077823
Y1: 224396622703251576439

I’m assuming you used msieve-GPU to search - what range are you searching?

Gimarel · 2019-05-27, 14:23

Quote:

Originally Posted by swellman

I’m assuming you used msieve-GPU to search - what range are you searching?

I run two instances to fully use the GPU. One starting from 100000000, the second starting from 200000000 for all coefficiants divisible by 120120.
I'm still trying to find the best stage1_norm. Currently I'm using 5e30.

2019-05-20, 20:14	#1
VBCurtis "Curtis" Feb 2005 Riverside, CA 1001001111100₂ Posts	Poly select and planning for 2,2330M Poly select and ECM have finished for 2330L, so we're on to begin factorization of 2330M: Code: 201916700580745604776027022665471186255107062245932082076863383752096343903385041484073267281054478199044604641397575671739630499971150912819790916215008125554106571022882316742647109864486081319721103021177161 We don't know who will factor this number, but NFS@home and forum-team-CADO are both reasonable choices; either way, a good poly will help get the number into NFS. On 2330L, Vebis did extensive CADO searching. He found a deg 6 at 1.94e-15, and deg 5 at 1.76e-15 (both after Max' spin efforts, which even he found lucky). Vebis also found a 1.65e-15 with CADO, which was not significantly changed by spin (1.66 best, I believe). Vebis' efforts were close to 4 core-years of poly select!!! By traditional measures, too much; however, he did deg 6 first and then learned that we expected deg 5 to be better, so repeated his search on deg 5. msieve-GPU deg 5 produced quite a few hits in the 1.40's, none of which spun into 1.60s so none were test-sieved. This C210 is roughly 50% harder than the C207 of 2330L. Poly scores around 1e-15 deg 5 before spin are good hits, 1.1e-15 for deg 6. The record score is deg 6, found by the CADO team for RSA210, at 1.49e-15. The CADO folks indicate deg 6 is preferred for this composite size, but experience in msieve is that deg 5 is more likely to produce a better poly. So, I suggest CADO folks aim at deg 6, msieve-gpu folks at deg 5. Naturally, anyone can do what they like, and any software/degree combo surely can produce the winning polynomial. As always, please post your search range to this thread before you search, to reduce overlapping efforts among contributors. Last fiddled with by VBCurtis on 2019-05-20 at 20:25

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2019-05-22, 22:52	#2
VBCurtis "Curtis" Feb 2005 Riverside, CA 2²·7·13² Posts	I am poly selecting with CADO: deg 5 admin 10M admax 20M with nq = 15625 and incr = 4620. These are the settings that produced the best pre-spin score from Vebis' work on 2330L. It'll be a few days.

2019-05-23, 15:17	#4
VBCurtis "Curtis" Feb 2005 Riverside, CA 2²·7·13² Posts	I believe the "long time" is caused by sopteffort set to 20. If you delete that, you should be OK. I'm running 4-threaded without specifying sopteffort and a 10M range is going to take around 6 days, so your reservation would be around 12-thread-days (I'm using all hyperthreads of an i7, so a non-HT machine would be about half this time). Also, note that adrange = incr means there is just one c5 value to test in each workunit, but default workers are 2-threaded. If you use adrange = 4 * incr = 18480 the workers will balance better and more fully utilize the threads allocated.

2019-05-23, 16:52	#5
Dylan14 "Dylan" Mar 2017 3·191 Posts	Ok, I have removed the sopteffort line and adjusted adrange in my params file and I will carry on with the reservation. I'm running it on a i5-6400 (4c, 4t) which is also running mmff, so I will keep you posted on progress. By the way, this is the largest number that I have tried to find a poly for.

2019-05-23, 21:30	#6
VBCurtis "Curtis" Feb 2005 Riverside, CA 2²×7×13² Posts	I appreciate your effort to help out, Dylan!

2019-05-25, 23:24	#8
VBCurtis "Curtis" Feb 2005 Riverside, CA 2²·7·13² Posts	cownoise says: skew 239563346.43219 score 8.00005243e-16 I'll have a poly Tuesday.