G197

fivemack · 2011-07-08, 08:38

After more than two months of polynomial searching (contributed particularly by bdodson), and trial-sieving about 200 candidates, I've come up with what I think is the best polynomial for the 197-digit cofactor of 7^374+1, namely

Code:

# norm 1.748068e-19 alpha -8.861264 e 5.627e-15 rroots 3
skew: 364380251.54
c0:  4348541943020307432834531575431557582005296059208
c1: -626624655839261549230516300510260244794696
c2:  1853996443926010028387831301890264
c3:  19250478525296406872044059
c4: -6615815776509564
c5:  7851060
Y0: -95132171124790181824704637743510497691
Y1:  2130029229416788788241
n: 61173781879800813987062254208969082152381029438415262556799619943895079615422740343994343770534689647933527791161943080608113058309486560791550732809340767016424578028793088881479019117986214217881
lpbr: 32
lpba: 33
mfbr: 64
mfba: 96
rlambda: 2.6
alambda: 3.6
alim: 240000000
rlim: 240000000

and a measurement of the correlation between Murphy score and time-to-sieve metrics which is much looser than I had expected.

We'd need to use the 16e siever, and start by sieving 80M to 400M. Yield is about two relations every three CPU-seconds (on 1900MHz Opteron), so that will be about a billion CPU-seconds in total on such a machine. This is a job large enough that only people with 64-bit Linux machines will be able to contribute usefully; I would also recommend dividing your range into quite small intervals, since I saw a 0.3% rate of hanging per 2kQ in gnfs-lasieve4I16e during the trial-sieving stage.

I suspect that the resources of the forum will be enough to get the sieving done by Christmas; and indeed it was done by 25 October, mostly thanks to bdodson.

Reservations
fivemack 08/07 80M - 89.6M (done 07/08)
fivemack 07/08 89.6M - 100.0M (done 27/09)
bdodson 15/07 200M - 300M (done mid-August, uploaded around 14 September)
bdodson 24/08 300M - 350M (uploaded 15 September)
bdodson 14/09 350M - 400M (uploaded 28 September)
bdodson 20/09 100M - 150M (uploaded 6 October)
bdodson 20/09 150M - 190M (extended 6 October from 150-170; uploaded 14 October)
fivemack 27/09 190M - 200M (finished 0130 25 October)
bdodson 07/10 400M - 450M (uploaded 24 October)

R.D. Silverman · 2011-07-11, 17:03

Quote:

Originally Posted by fivemack

After more than two months of polynomial searching (contributed particularly by bdodson), and trial-sieving about 200 candidates, I've come up with what I think is the best polynomial for the 197-digit cofactor of 7^374+1, namely

Code:

# norm 1.748068e-19 alpha -8.861264 e 5.627e-15 rroots 3
skew: 364380251.54
c0:  4348541943020307432834531575431557582005296059208
c1: -626624655839261549230516300510260244794696
c2:  1853996443926010028387831301890264
c3:  19250478525296406872044059
c4: -6615815776509564
c5:  7851060
Y0: -95132171124790181824704637743510497691
Y1:  2130029229416788788241
n: 61173781879800813987062254208969082152381029438415262556799619943895079615422740343994343770534689647933527791161943080608113058309486560791550732809340767016424578028793088881479019117986214217881
lpbr: 32
lpba: 33
mfbr: 64
mfba: 96
rlambda: 2.6
alambda: 3.6
alim: 240000000
rlim: 240000000

and a measurement of the correlation between Murphy score and time-to-sieve metrics which is much looser than I had expected.

We'd need to use the 16e siever, and start by sieving 80M to 400M. Yield is about two relations every three CPU-seconds (on 1900MHz Opteron), so that will be about a billion CPU-seconds in total on such a machine. This is a job large enough that only people with 64-bit Linux machines will be able to contribute usefully; I would also recommend dividing your range into quite small intervals, since I saw a 0.3% rate of hanging per 2kQ in gnfs-lasieve4I16e during the trial-sieving stage.

I suspect that the resources of the forum will be enough to get the sieving done by Christmas.

Reservations
fivemack 08/07 80M - 89.6M

I am a bit surprised that the rational and algebraic factor bases have the
same size.. Did you run some trial sieving? I would have guessed that the
algebraic side would have the larger factor base.

frmky · 2011-07-11, 18:12

Quote:

Originally Posted by R.D. Silverman

I am a bit surprised that the rational and algebraic factor bases have the
same size.. Did you run some trial sieving? I would have guessed that the
algebraic side would have the larger factor base.

To offset this, three large primes are allowed on the algebraic side but only two on the rational side. This allows for a smaller factor base and therefore lower memory use during sieving. However, I have noticed that for NFS@Home SNFS targets this does increase the number of duplicate relations somewhat from typically ~23% for two large primes on both sides to ~30% for three large primes on one side.

bdodson · 2011-07-14, 18:56

Quote:

Originally Posted by fivemack

After more than two months of polynomial searching (contributed particularly by bdodson), and trial-sieving about 200 candidates, I've come up with what I think is the best polynomial for the 197-digit cofactor of 7^374+1, ...

We'd need to use the 16e siever, and start by sieving 80M to 400M. ...

I'll start with 200M-300M, while our disks are crowded with data for the matrices
on two completed sieving tasks. -Bruce

bdodson · 2011-07-15, 06:32

Quote:

Originally Posted by bdodson

I'll start with 200M-300M, while our disks are crowded with data for the matrices
on two completed sieving tasks. -Bruce

This one also uses -M 1 (like 2p956)? And we're only sieving on the
algebraic side? -bd

fivemack · 2011-07-15, 09:55

Yes: sieve on the algebraic side only. I .think. that -M 1 is set by default, but there's no harm in using it if it isn't.

bdodson · 2011-07-16, 13:53

Quote:

Originally Posted by fivemack

Yes: sieve on the algebraic side only. I .think. that -M 1 is set by default, but there's no harm in using it if it isn't.

Yes (same as it was for 956 ...). None of the first 1000 tasks of width 4K
from 200M-210M got hung (with Serge's March 2010 binary). So far, so good.

-Bruce

jyb · 2011-07-17, 03:33

Quote:

Originally Posted by fivemack

After more than two months of polynomial searching (contributed particularly by bdodson), and trial-sieving about 200 candidates, I've come up with what I think is the best polynomial for the 197-digit cofactor of 7^374+1, namely

[snip]

We'd need to use the 16e siever, and start by sieving 80M to 400M. Yield is about two relations every three CPU-seconds (on 1900MHz Opteron), so that will be about a billion CPU-seconds in total on such a machine.

[snip]

As a sanity-check, can somebody tell me what yield I should be seeing (in relations/q, not relations/sec). I did a trial-sieve with this .poly file of just 1000, starting at 341M (i.e. -f 341000000 -c 1000), and I got way fewer relations than I would have expected. WAY fewer. Can anybody tell me how many I should have gotten?

fivemack · 2011-07-17, 11:12

I'm running the range at the moment to check; it's not complete yet, but I would expect about 1800 relations by simple extrapolation.

edit: job complete; total yield: 2183, q=341001007 (1.72407 sec/rel)

The build of gnfs-lasieve4I16e that I'm using is at http://www.chiark.greenend.org.uk/~t...s-lasieve4I16e

jyb · 2011-07-18, 15:57

Quote:

Originally Posted by fivemack

I'm running the range at the moment to check; it's not complete yet, but I would expect about 1800 relations by simple extrapolation.

edit: job complete; total yield: 2183, q=341001007 (1.72407 sec/rel)

The build of gnfs-lasieve4I16e that I'm using is at http://www.chiark.greenend.org.uk/~t...s-lasieve4I16e

Okay, thanks for that. There's definitely something wrong on my end. I think I built the gnfs-lasieve* binaries a long time ago, so they're using an old version of the source. Guess I'd better update to latest and rebuild them.

chris2be8 · 2011-07-21, 09:05

Quote:

Originally Posted by fivemack

The build of gnfs-lasieve4I16e that I'm using is at http://chiark.greenend.org.uk/~twoma...s-lasieve4I16e

That link doesn't work for me.

fivemack: fixed now

I get a page saying:

Quote:

Sorry, wrong server address
chiark's webserver is at http://www.chiark.greenend.org.uk.

Please add the www to the URL you were using and try again; if you got to this page by following a link please inform the owner of the page you came from so that they can correct the link.
Ian Jackson webmaster@chiark.greenend.org.uk.

Chris K

2011-07-08, 08:38	#1
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 7²·131 Posts	G197 After more than two months of polynomial searching (contributed particularly by bdodson), and trial-sieving about 200 candidates, I've come up with what I think is the best polynomial for the 197-digit cofactor of 7^374+1, namely Code: # norm 1.748068e-19 alpha -8.861264 e 5.627e-15 rroots 3 skew: 364380251.54 c0: 4348541943020307432834531575431557582005296059208 c1: -626624655839261549230516300510260244794696 c2: 1853996443926010028387831301890264 c3: 19250478525296406872044059 c4: -6615815776509564 c5: 7851060 Y0: -95132171124790181824704637743510497691 Y1: 2130029229416788788241 n: 61173781879800813987062254208969082152381029438415262556799619943895079615422740343994343770534689647933527791161943080608113058309486560791550732809340767016424578028793088881479019117986214217881 lpbr: 32 lpba: 33 mfbr: 64 mfba: 96 rlambda: 2.6 alambda: 3.6 alim: 240000000 rlim: 240000000 and a measurement of the correlation between Murphy score and time-to-sieve metrics which is much looser than I had expected. We'd need to use the 16e siever, and start by sieving 80M to 400M. Yield is about two relations every three CPU-seconds (on 1900MHz Opteron), so that will be about a billion CPU-seconds in total on such a machine. This is a job large enough that only people with 64-bit Linux machines will be able to contribute usefully; I would also recommend dividing your range into quite small intervals, since I saw a 0.3% rate of hanging per 2kQ in gnfs-lasieve4I16e during the trial-sieving stage. I suspect that the resources of the forum will be enough to get the sieving done by Christmas; and indeed it was done by 25 October, mostly thanks to bdodson. Reservations fivemack 08/07 80M - 89.6M (done 07/08) fivemack 07/08 89.6M - 100.0M (done 27/09) bdodson 15/07 200M - 300M (done mid-August, uploaded around 14 September) bdodson 24/08 300M - 350M (uploaded 15 September) bdodson 14/09 350M - 400M (uploaded 28 September) bdodson 20/09 100M - 150M (uploaded 6 October) bdodson 20/09 150M - 190M (extended 6 October from 150-170; uploaded 14 October) fivemack 27/09 190M - 200M (finished 0130 25 October) bdodson 07/10 400M - 450M (uploaded 24 October) Last fiddled with by fivemack on 2011-10-25 at 09:45

2011-07-17, 11:12	#9
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 7²×131 Posts	I'm running the range at the moment to check; it's not complete yet, but I would expect about 1800 relations by simple extrapolation. edit: job complete; total yield: 2183, q=341001007 (1.72407 sec/rel) The build of gnfs-lasieve4I16e that I'm using is at http://www.chiark.greenend.org.uk/~t...s-lasieve4I16e Last fiddled with by fivemack on 2011-07-21 at 18:42

2011-07-15, 09:55	#6
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 7²·131 Posts	Yes: sieve on the algebraic side only. I .think. that -M 1 is set by default, but there's no harm in using it if it isn't.