2^877-1 polynomial selection

fivemack · 2009-06-01, 17:58

Another month, another 17x-digit GNFS.

Pick a number between zero and 1000 which hasn't been picked before, and post saying which you've picked; as far as I know, you're no more likely to find a good polynomial in any range than in any other. I will use '389' as the example number.

Put the line

Code:

N 2426823897740521871358050077978548270356369169858920055316001626238737543956741884688508977082673772430933692083180285944173725894314917788842645762469500115886775910459988933319

into a file called something like M877.389.data

Obtain (from http://www.mersenneforum.org/showpos...10&postcount=2, or by building them yourself from ggnfs svn) the pol51m0b and pol51opt executables.

Run

Code:

pol51m0b -b M877.389 -p 8 -n 1.7e26 -a 38900000 -A 39000000

ie -a 100000X -A 100000(1+X)

which will take about 14 hours on one core2/2400 core (NB it's much quicker for smaller ranges, only about three hours for range 000) and produce a file M877.389.51.m with between a few hundred and a few thousand lines.

Run

Code:

pol51opt -n 1.3e26 -N 2e23 -b M877.389 -e 7.0e-14

which will take between a few hours and a few dozen hours, and will produce a file M877.389.cand with a widely variable number of lines, consisting of lots of blocks of the form

Code:

BEGIN POLY #skewness 302984.00 norm 7.07e+24 alpha -5.07 Murphy_E 7.08e-14
X5 38902471200
X4 -175620852038927313
X3 26362636095106986685408
X2 -4619269142557809418631719430
X1 -935036711601700177680636473088168
X0 50242391282148099865092144031788410688
Y1 7163709297211109687
Y0 -2285663093636710791536341014657281
M 720342180002848932822665197147412139722267501887950287595140130145869592769744535047190636191707397163967515655793706388645419869266262883407109959170159333145235003312628195150

If there are any lines beginning 'BEGIN POLY' in M877.389.cand with a Murphy_E value greater than or equal to the best one posted here so far (your favourite platform's equivalent to

Code:

grep urph M877.389.cand | sort -g -k 10 | tail

may help), post the whole block here; I'll do test sieving on them all and see which has the largest real-world yield.

Repeat the whole process until June 18th or until you're fed up.

I suspect there's a polynomial with a score better than 1.1e-13 to be found, and every 0.01e-14 improvement in the score will save us several dozen CPU-hours at the sieving stage; we'll start sieving on Midsummer's Day with the best polynomial that's been found by June 18th

Reservations
antiroach 0-5 done 8.15e-14
antiroach 5-20 except 14 done nothing of interest
axn 14 done 8.26e-14
frmky 20-112 except 28, 47 and 56 done nothing of interest
axn 28 done 7.38e-14
andi47 47 done 7.35e-14
axn 56 done nowt
axn 112 done nowt
frmky 113-200 done nothing of interest
smh 200 done nowt
fivemack 200-224 done 9.23e-14
axn 224 done 7.59e-14
frmky 225-300 nothing of interest
frmky 300-360 done 8.92e-14
frmky 360-380 done 8.03e-14
fivemack 380-400 done 8.25e-14
fivemack 400-500 done 9.21e-14
frmky 500-600 done 9.20e-14
frmky 600-800
fivemack 800-1000
fivemack 1000-1200 done 8.87e-14
fivemack 1200-1260 done 8.39e-14
fivemack 1260-1300

R.D. Silverman · 2009-06-01, 18:14

Quote:

Originally Posted by fivemack

Another month, another 17x-digit GNFS.

Pick a number between zero and 1000 which hasn't been picked before, and post saying which you've picked; as far as I know, you're no more likely to find a good polynomial in any range than in any other. I will use '389' as the example number.

Put the line

Code:

N 2426823897740521871358050077978548270356369169858920055316001626238737543956741884688508977082673772430933692083180285944173725894314917788842645762469500115886775910459988933319

into a file called something like M877.389.data

Obtain (from http://www.mersenneforum.org/showpos...10&postcount=2, or by building them yourself from ggnfs svn) the pol51m0b and pol51opt executables.

Run

Code:

pol51m0b -b M877.389 -p 8 -n 1.7e26 -a 38900000 -A 39000000

ie -a 100000X -A 100000(1+X)

which will take about 14 hours on one core2/2400 core (NB it's much quicker for smaller ranges, only about three hours for range 000) and produce a file M877.389.51.m with between a few hundred and a few thousand lines.

Run

Code:

pol51opt -n 1.3e26 -N 2e23 -b M877.389 -e 7.0e-14

which will take between a few hours and a few dozen hours, and will produce a file M877.389.cand with a widely variable number of lines, consisting of lots of blocks of the form

Code:

BEGIN POLY #skewness 302984.00 norm 7.07e+24 alpha -5.07 Murphy_E 7.08e-14
X5 38902471200
X4 -175620852038927313
X3 26362636095106986685408
X2 -4619269142557809418631719430
X1 -935036711601700177680636473088168
X0 50242391282148099865092144031788410688
Y1 7163709297211109687
Y0 -2285663093636710791536341014657281
M 720342180002848932822665197147412139722267501887950287595140130145869592769744535047190636191707397163967515655793706388645419869266262883407109959170159333145235003312628195150

If there are any lines beginning 'BEGIN POLY' in M877.389.cand with a Murphy_E value greater than or equal to the best one posted here so far (your favourite platform's equivalent to

Code:

grep urph M877.389.cand | sort -g -k 10 | tail

may help), post the whole block here; I'll do test sieving on them all and see which has the largest real-world yield.

Repeat the whole process until June 18th or until you're fed up.

I suspect there's a polynomial with a score better than 1.1e-13 to be found, and every 0.01e-14 improvement in the score will save us several dozen CPU-hours at the sieving stage; we'll start sieving on Midsummer's Day with the best polynomial that's been found by June 18th

Reservations

fivemack 380-400

Will GNFS be faster than SNFS? It is close.

frmky · 2009-06-01, 19:30

frmky 360-380

antiroach · 2009-06-01, 19:37

antiroach 0-5

Is there a way to track progress when running pol51m0b?

frmky · 2009-06-02, 03:07

Quote:

Originally Posted by frmky

frmky 360-380

That went much more quickly than expected. The best poly was

Code:

BEGIN POLY #skewness 882095.12 norm 7.89e+24 alpha -5.96 Murphy_E 8.03e-14
X5 37551413340
X4 -18912546537876037
X3 -113814576528461898290387
X2 10359196566616328061415711938
X1 31062438900126333398445772457845543
X0 -43103716967954269114239865122595502805
Y1 3785186493283328947
Y0 -2301878492779152102060887803551802
M 16793546605175154476732525265645227867084626485392719897672431260069383174679471313393931995945360183033878$
END POLY

I'll now reserve
frmky 300-360

axn · 2009-06-02, 03:43

Reserving 14 and 28

axn · 2009-06-02, 07:11

14 done. Reserving 56 (BTW, it is NOT 12,24)

Best is a 8.26. Second best is 7.71

Code:

BEGIN POLY #skewness 2079772.57 norm 6.16e+024 alpha -5.84 Murphy_E 8.26e-014
X5 1467231360
X4 13840631600912371
X3 -20518074718309616991592
X2 -23127033341910364722302550846
X1 40611190451383792230615253375297342
X0 6259244685376033177460376064968265982285
Y1 1733396567827630211
Y0 -4402586850256143045312923816672808
M 1127974133821908515271331948508183117127869869657001963831217889258458949658553855593125629438683729386138901328891688368946213153236864552790689946357410782499007463716679254683
END POLY

fivemack · 2009-06-02, 07:43

Quote:

Originally Posted by antiroach

antiroach 0-5

Is there a way to track progress when running pol51m0b?

Yes, do 'type M877.001.51.m' (on Windows, 'cat M877.001.51.m' on Unix) and see what the first number in the last line is

axn · 2009-06-02, 08:06

28 done. Nothing worth reporting, the best being a 7.38

Reserving 112.

axn · 2009-06-02, 10:46

56 done. Zero polynomials :-(

Reserving 224

axn · 2009-06-02, 12:30

112 done. Zero again.

2009-06-01, 17:58	#1
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 1936₁₆ Posts	2^877-1 polynomial selection Another month, another 17x-digit GNFS. Pick a number between zero and 1000 which hasn't been picked before, and post saying which you've picked; as far as I know, you're no more likely to find a good polynomial in any range than in any other. I will use '389' as the example number. Put the line Code: N 2426823897740521871358050077978548270356369169858920055316001626238737543956741884688508977082673772430933692083180285944173725894314917788842645762469500115886775910459988933319 into a file called something like M877.389.data Obtain (from http://www.mersenneforum.org/showpos...10&postcount=2, or by building them yourself from ggnfs svn) the pol51m0b and pol51opt executables. Run Code: pol51m0b -b M877.389 -p 8 -n 1.7e26 -a 38900000 -A 39000000 ie -a 100000X -A 100000(1+X) which will take about 14 hours on one core2/2400 core (NB it's much quicker for smaller ranges, only about three hours for range 000) and produce a file M877.389.51.m with between a few hundred and a few thousand lines. Run Code: pol51opt -n 1.3e26 -N 2e23 -b M877.389 -e 7.0e-14 which will take between a few hours and a few dozen hours, and will produce a file M877.389.cand with a widely variable number of lines, consisting of lots of blocks of the form Code: BEGIN POLY #skewness 302984.00 norm 7.07e+24 alpha -5.07 Murphy_E 7.08e-14 X5 38902471200 X4 -175620852038927313 X3 26362636095106986685408 X2 -4619269142557809418631719430 X1 -935036711601700177680636473088168 X0 50242391282148099865092144031788410688 Y1 7163709297211109687 Y0 -2285663093636710791536341014657281 M 720342180002848932822665197147412139722267501887950287595140130145869592769744535047190636191707397163967515655793706388645419869266262883407109959170159333145235003312628195150 If there are any lines beginning 'BEGIN POLY' in M877.389.cand with a Murphy_E value greater than or equal to the best one posted here so far (your favourite platform's equivalent to Code: grep urph M877.389.cand \| sort -g -k 10 \| tail may help), post the whole block here; I'll do test sieving on them all and see which has the largest real-world yield. Repeat the whole process until June 18th or until you're fed up. I suspect there's a polynomial with a score better than 1.1e-13 to be found, and every 0.01e-14 improvement in the score will save us several dozen CPU-hours at the sieving stage; we'll start sieving on Midsummer's Day with the best polynomial that's been found by June 18th Reservations antiroach 0-5 done 8.15e-14 antiroach 5-20 except 14 done nothing of interest axn 14 done 8.26e-14 frmky 20-112 except 28, 47 and 56 done nothing of interest axn 28 done 7.38e-14 andi47 47 done 7.35e-14 axn 56 done nowt axn 112 done nowt frmky 113-200 done nothing of interest smh 200 done nowt fivemack 200-224 done 9.23e-14 axn 224 done 7.59e-14 frmky 225-300 nothing of interest frmky 300-360 done 8.92e-14 frmky 360-380 done 8.03e-14 fivemack 380-400 done 8.25e-14 fivemack 400-500 done 9.21e-14 frmky 500-600 done 9.20e-14 frmky 600-800 fivemack 800-1000 fivemack 1000-1200 done 8.87e-14 fivemack 1200-1260 done 8.39e-14 fivemack 1260-1300 Last fiddled with by fivemack on 2009-06-13 at 17:00 Reason: add example

2009-06-01, 19:37	#4
antiroach Jun 2003 2²·61 Posts	antiroach 0-5 Is there a way to track progress when running pol51m0b? Last fiddled with by antiroach on 2009-06-01 at 19:39

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2009-06-01, 19:30	#3
frmky Jul 2003 So Cal 7×383 Posts	frmky 360-380

2009-06-02, 03:43	#6
axn Jun 2003 2·7·17·23 Posts	Reserving 14 and 28

2009-06-02, 08:06	#9
axn Jun 2003 12542₈ Posts	28 done. Nothing worth reporting, the best being a 7.38 Reserving 112.

2009-06-02, 10:46	#10
axn Jun 2003 12542₈ Posts	56 done. Zero polynomials :-( Reserving 224

2009-06-02, 12:30	#11
axn Jun 2003 12542₈ Posts	112 done. Zero again.