20130206, 12:26  #100 
Tribal Bullet
Oct 2004
2^{4}·13·17 Posts 
Their best is 3.51e19; the full 5000 will probably take 5 days on one core

20130206, 18:55  #101 
Sep 2009
1721_{8} Posts 
Size optimization finished on batch 1 (nearly 48h wallclock time for 4 processes on Xeon E31230, 2 processes finished ~30' earlier) and batch 8 (~44h30 wall clock time for 8 processes on FX8150; 6 processes finished 2h earlier).
FWIW, both runs used MPIpatched msieve with a single .dat.m input file, so poily's latest patch works for me MPI root optimization has started. EDIT: BTW, poily, it would be great to make the same kind of change for root optimization as you did for size optimization: the ability to trigger multiprocess root optimization from a single input file, if no .dat.ms.mpi* files are found Last fiddled with by debrouxl on 20130206 at 19:29 
20130207, 05:41  #102 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3·29·83 Posts 
I suddenly have two more cores that are free, so I'm taking batch 6. (I suppose it will take 4 days to do, using half the cores.)
PS If we do the root sieve, do you want the sizeopt hits as well as the final polys? Edit: When using `split n`, be sure to right `split n l/2` as opposed to `split n 2`. That doesn't split lines Last fiddled with by Dubslow on 20130207 at 06:20 
20130207, 18:22  #103 
Apr 2010
Over the rainbow
100111101000_{2} Posts 
i'm far from being done, but so far best poly give 2.837e019
Code:
# norm 5.520074e020 alpha 12.511594 e 2.837e019 rroots 4 skew: 81766141.19 c0: 3607869805213281554823252296618828604677914930359987025344 c1: 23220164568489045138114308221677930169305838193010240 c2: 9203124297129543437723323024998562111194036 c3: 9334995343944464727631510927880010416 c4: 324816754181582556026397511033 c5: 2223278394876459083044 c6: 7232286821760 Y0: 6203084729795742043403960083120441126010795 Y1: 42260925725431380236248723 
20130208, 07:55  #104 
Sep 2009
977 Posts 
The three best polys, in batch 1 (processed by the Xeon E31230 with 8 processes in ~29h wall clock time, 7 of the 8 processes finished at 1617h) are
Code:
# norm 6.453437e20 alpha 12.047099 e 3.248e19 rroots 6 skew: 84355332.37 c0: 40946290090445266551161549499305741933274180644750016085425 c1: 10467357875909381144128954908126047238982795499683785 c2: 575409405642562087310720821835776371535397053 c3: 9572582929973485805475819618000250061 c4: 148894749080944910994034682372 c5: 724347752270183267004 c6: 1859803545600 Y0: 7778737956208683626717082871144859356558432 Y1: 10686505327134712299646993 Code:
# norm 6.056026e20 alpha 11.631907 e 3.052e19 rroots 4 skew: 48793635.82 c0: 9335896655809604327925621788999250854933506382363022965344 c1: 1925306846817736254699271114907020489847742878092288 c2: 169310545848405710260883307959917839585756986 c3: 3496004302313744686041859045254926483 c4: 275085812586209584750675391032 c5: 1408333791906605513980 c6: 478010332800 Y0: 9755452962557811620933593496014011645343335 Y1: 4282423141698728009631007 Code:
# norm 5.969626e20 alpha 11.556799 e 3.019e19 rroots 6 skew: 47942131.68 c0: 18012875627631792901670781168326202449068477209742252483200 c1: 1457681444502169713650799905383394058738666204734748 c2: 139260042798502345861170120050843951277513880 c3: 5797429652761017495601014198560882931 c4: 259974699150207277836260389632 c5: 1402165548484195645180 c6: 478010332800 Y0: 9755452962567021682782058132587572724643997 Y1: 4282423141698728009631007 Code:
# norm 6.632671e20 alpha 11.607950 e 2.967e19 rroots 4 skew: 49069361.13 c0: 28745311041103203356576951005989940082831495232341768515776 c1: 205998030496036644387588200533512340837882272321360 c2: 132018394189437555571701225591789662744633256 c3: 1365610013934000246262086253251260366 c4: 19443724695135903573441283643 c5: 392511937028479386086 c6: 5858173601280 Y0: 6424804940317563889082609710168513250186575 Y1: 451681905409118609701262291 
20130208, 09:42  #105 
"Nancy"
Aug 2002
Alexandria
2,467 Posts 

20130208, 10:01  #106 
Apr 2010
Over the rainbow
2^{3}·317 Posts 
and what does it say about my personality? (no seriously... what does the low alpha mean? I won't ask about double rainbow, don't worry)
and for the sake of it my lowest alpha value Code:
# norm 4.628932e020 alpha 12.956412 e 2.448e019 rroots 4 skew: 111461741.54 c0: 4596185303540975912941768799404404251911067990661592486450560 c1: 280987050579580684349518348073004894589766436497544888 c2: 5453326966044145207308567141134658983582007302 c3: 92528123968159463596593396717045851089 c4: 560963993141923165266152827450 c5: 2978793911777564174904 c6: 6711846261120 Y0: 6280776226247745384246196650168744854827871 Y1: 80764498754829792133232269 Code:
# norm 5.554255e020 alpha 12.726487 e 2.853e019 rroots 4 skew: 88161163.72 c0: 592294109350104075885455758432520983785765035911272504595840 c1: 44228198432626906079450591344684081042731028765034896 c2: 1266780839981054007483109448136912523638841412 c3: 25584881562241130646568639974012624680 c4: 32136804857417066806626443393 c5: 3165936771052409436964 c6: 7232286821760 Y0: 6203084730713792276611133070779722382751981 Y1: 42260925725431380236248723 Last fiddled with by firejuggler on 20130208 at 10:19 
20130208, 11:49  #107 
"Nancy"
Aug 2002
Alexandria
2,467 Posts 
The alpha value is a measure for how many very small prime factors the polynomial values contain on average. We are looking for smooth polynomial values (= no large prime factors), and there will be more of those in the search region if the polynomial values tend to contain a lot of very small primes. The alpha value tells that, thanks to having many small primes, polynomial values F(a,b) are about as likely smooth as as an integer around F(a,b)*exp(alpha), so with alpha=12, the polynomial values are about as likely to be smooth as if they were smaller by a factor of ~16000.
Last fiddled with by akruppa on 20130208 at 13:32 Reason: of>if. Edit: ah, I had not taken into consideration that this was a deg 5 vs. deg 6 issue. thanks Jason! 
20130208, 12:31  #108 
Nov 2010
2·5^{2} Posts 
Hm, I was under impression the patch should also work for poly root optimization... But it didn't due to copypaste mistype, here's fixed version of the patch.
I finished the batch 7, started poly root optimization of best 5000. 
20130208, 13:07  #109 
Tribal Bullet
Oct 2004
2^{4}×13×17 Posts 
The other thing that really jumps out at me from the list of best polynomials is that all of them are coming from stage 1 hits found by the CADO tools. I think the Msieve hits are the ones with lots of highorder zeroes in the leading algebraic coefficient, and in all the stage 2 that I've run locally the best E value I've been able to find from an Msieve stage 1 hit is around 3e19.
Paul has been suggesting that targeting a leading rational coefficient size that is somewhat smaller than the maximum possible, for a given choice of stage 1 size bound, gives a better chance of a good polynomial after size optimization. Looks like I should try a few experiments. I think all of modern GNFS polynomial selection is basically a struggle to increase the amount of skew without making stage 1 stop working; the end result is a playground of absurd alpha values. It doesn't hurt that the playground is enormously larger now that we're in degree6 territory (an alpha value < 5 is still pretty unusual for degree5 polynomials). Shi Bai's dissertation found that for RSA768 a large sampling of sizeoptimized polynomials had a mean alpha value of 0.2 and standard deviation of about 0.8; so finding an alpha value of say 10.0 is a 12sigma event. Last fiddled with by jasonp on 20130208 at 13:21 
20130209, 06:53  #110 
Jul 2003
So Cal
2,083 Posts 
Here's another 9.5 million. I've stopped it for now.
https://www.dropbox.com/s/meef9g9dkq...896_4.dat.m.gz 
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