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Old 2009-06-01, 17:58   #1
fivemack
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Default 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
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Old 2009-06-01, 18:14   #2
R.D. Silverman
 
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Quote:
Originally Posted by fivemack View Post
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.
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Old 2009-06-01, 19:30   #3
frmky
 
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frmky 360-380
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Old 2009-06-01, 19:37   #4
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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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Old 2009-06-02, 03:07   #5
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Quote:
Originally Posted by frmky View Post
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
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Old 2009-06-02, 03:43   #6
axn
 
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Reserving 14 and 28
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Old 2009-06-02, 07:11   #7
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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
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Old 2009-06-02, 07:43   #8
fivemack
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Quote:
Originally Posted by antiroach View Post
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

Last fiddled with by fivemack on 2009-06-02 at 07:43
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Old 2009-06-02, 08:06   #9
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28 done. Nothing worth reporting, the best being a 7.38

Reserving 112.
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Old 2009-06-02, 10:46   #10
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56 done. Zero polynomials :-(

Reserving 224
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Old 2009-06-02, 12:30   #11
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112 done. Zero again.
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