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 2005-01-11, 22:16 #1 garo     Aug 2002 Termonfeckin, IE 53058 Posts 12- table Code: Size Base Index Mod Diff Ratio 335 12 311 - 335.6 0.998 283 12 313 - 337.7 0.837 260 12 319 - 312.9 0.83 /11 290 12 331 - 357.2 0.811 265 12 337 - 363.6 0.727 345 12 347 - 374.4 0.921 Last fiddled with by Batalov on 2021-01-05 at 18:00 Reason: 12,343- is done
 2005-08-08, 21:07 #2 rogue     "Mark" Apr 2003 Between here and the 141448 Posts Here are current curve counts for this table: 12,299- B 11000000 1751 12,299- B 110000000 297 12,227- B 11000000 4522 12,269- B 11000000 4581 12,259- B 11000000 4481 12,259- B 110000000 22 12,247- B 11000000 4616 12,247- B 43000000 6 12,233- B 11000000 4741 12,295- B 11000000 4676 12,271- B 11000000 4668 12,229- B 11000000 4610 12,229- B 43000000 4 12,241- B 11000000 4347 12,241- B 110000000 7 12,257- B 11000000 4472 12,277- B 11000000 3840 12,293- B 11000000 4515 12,293- B 110000000 6 12,281- B 11000000 3665 12,289- B 11000000 4376 12,283- B 11000000 4050 I'm stopping on this now.
 2008-02-26, 14:20 #3 hlaiho     Feb 2005 29 Posts 12,229- completed According to: http://www.loria.fr/%7Ezimmerma/records/c120-355 CWI has completed 12^229-1 by SNFS , the second largest factor is 5614625825187525959903363633922994959000986456830889529904105379 Last fiddled with by hlaiho on 2008-02-26 at 14:21
 2008-02-28, 12:51 #4 R.D. Silverman     Nov 2003 1D2416 Posts Filtering Weirdness I encountered something strange when filtering 2,776+. Sieving is nearly done and I ran a trial filtering pass last night. The first pass was done with mergelevel 2 and filtmin = 18.8million (corresponding to 1.2 million ideals per polynomial below 18.8M). Some duplicates had already been removed. Here is the output from the first pass. ======================================================== Maximum number of shrinkage passes executed. Start final pass at Mon Feb 25 18:43:31 2008 after 10061.053 seconds. 15233697 duplicate relations were detected. 58419 relation-sets were discarded because they are too heavy. Output file has 22891386 relations in 21850372 sets. Another 155388 free relations on large primes available. There may be additional free relations on factor base primes. Net 22005760 equations on 13108742 large prime ideals in [18800000, 1000000000]. 3924632 relation-sets have exactly 0.0 relations (frees count 0.5). 15276016 relation-sets have exactly 1.0 relations (frees count 0.5). 43507 relation-sets have exactly 1.5 relations (frees count 0.5). 1491504 relation-sets have exactly 2.0 relations (frees count 0.5). 31578 relation-sets have exactly 2.5 relations (frees count 0.5). 529280 relation-sets have exactly 3.0 relations (frees count 0.5). 23328 relation-sets have exactly 3.5 relations (frees count 0.5). 230061 relation-sets have exactly 4.0 relations (frees count 0.5). 17580 relation-sets have exactly 4.5 relations (frees count 0.5). 113312 relation-sets have exactly 5.0 relations (frees count 0.5). 13447 relation-sets have exactly 5.5 relations (frees count 0.5). 60413 relation-sets have exactly 6.0 relations (frees count 0.5). 10027 relation-sets have exactly 6.5 relations (frees count 0.5). 34220 relation-sets have exactly 7.0 relations (frees count 0.5). 7611 relation-sets have exactly 7.5 relations (frees count 0.5). 20788 relation-sets have exactly 8.0 relations (frees count 0.5). 5954 relation-sets have exactly 8.5 relations (frees count 0.5). 12764 relation-sets have exactly 9.0 relations (frees count 0.5). 4350 relation-sets have exactly 9.5 relations (frees count 0.5). Row weight Frequency Cum freq Cum wght pct 1 25 25 0.00 2 65 90 0.00 ======================================================== There seems to be an excess of 8897018 = 22005760 - 13108742 equations at this point. No doubt some of them arise from duplicate relations, so the next pass was run with mergelevel 0. Sure enough, it found a fair number of duplicates: ==================================================== # Filter part of Number Field Sieve Initializing hash table (duplicates) with 43875001 entries... Starting nfs.fin1. 0 relations in 0 sets after 0.152 seconds. Duplicate relation found: a=-233572, b=13353 Read 22728574 relations in 22728574 sets in 384.829 seconds. Freeing hash table... 5008788 duplicate relations were detected. 0 relation-sets were discarded because they are too heavy. Output file has 17719786 relations in 17719786 sets. ====================================================== So of the 8897M execess equations, 5008M arise from duplicates. This is fine, because it still leaves an excess of 8.897 - 5.008 = 3.889M excess equations. 2.4million are needed to take care of the ideals BELOW 18.8 million, so it seems that I still have an excess of 3.889-2.400 = 1.489M equations . These get removed with higher merge level passes. However, before I do the higher merge levels, I always do another pass with mergelevel 2 after removing the duplicates. And I got a BIG SURPRISE: ====================================================== # Filter part of Number Field Sieve # X86 (Windows) $Revision: 1.44$ $Date: 2003/05/27 00:20:02$ # Department of Mathematics, Oregon State University Maximum number of shrinkage passes executed. Start final pass at Mon Feb 25 20:13:24 2008 after 4607.354 seconds. 0 duplicate relations were detected. 220471 relation-sets were discarded because they are too heavy. Output file has 14360944 relations in 7953642 sets. Another 102666 free relations on large primes available. There may be additional free relations on factor base primes. Net 8056308 equations on 8259014 large prime ideals in [18800000, 1000000000]. ===================================================== I now have a DEFICIT! This final filter pass discarded 220K relations because they were too heavy, but I thought that I had an excess of 1.489M to begin with! Where did the excess go???
2008-02-28, 12:58   #5
R.D. Silverman

Nov 2003

746010 Posts

Quote:
 Originally Posted by R.D. Silverman I encountered something strange when filtering 2,776+. Sieving is nearly done and I ran a trial filtering pass last night. The first pass was done with mergelevel 2 and filtmin = 18.8million (corresponding to 1.2 million ideals per polynomial below 18.8M).

A followup. I gathered another 1.5M relations over the last two days.
After the first filter pass, I had an excess of 9.65million equations.
5.45M of these were duplicates, leaving 4.2million in excess.
Another filter pass with mergelevel 2 then gave 9.2million equations
on 9million ideals over 18.8million; i.e. an excess of 200K.
too heavy. However, 4.2million - 350K = 3.85million. 2.4 million
are needed to take care of the ideals below 18.8 million, so I should
have an excess of 1.45million and not an excess of 200K.

Where did the rest go????

2008-02-28, 14:47   #6
jasonp
Tribal Bullet

Oct 2004

2·3·19·31 Posts

Quote:
 Originally Posted by R.D. Silverman I now have a DEFICIT! This final filter pass discarded 220K relations because they were too heavy, but I thought that I had an excess of 1.489M to begin with! Where did the excess go???
Does merge level 2 create relation sets out of relations that have ideals of weight 2? The filtering deleted 220k relation sets, could those sets contain a huge number of relations somehow? Also, when does singleton removal happen in this scheme, and can it be responsible for deleting many more relations than ideals? Finally, 25% duplicates sounds like a lot, maybe you needed to do a lot more sieving and the removed duplicates turned many ideals into singletons.

Last fiddled with by jasonp on 2008-02-28 at 14:48

2008-02-28, 15:26   #7
R.D. Silverman

Nov 2003

22·5·373 Posts

Quote:
 Originally Posted by jasonp Does merge level 2 create relation sets out of relations that have ideals of weight 2? The filtering deleted 220k relation sets, could those sets contain a huge number of relations somehow? Also, when does singleton removal happen in this scheme, and can it be responsible for deleting many more relations than ideals? Finally, 25% duplicates sounds like a lot, maybe you needed to do a lot more sieving and the removed duplicates turned many ideals into singletons.

Merge level two only means that at most 2 relations are combined into 1.
Singleton removal happens in the first pass.

Some duplicates (5M) were removed prior to the first filtering pass.
15M duplicates got removed in the first pass.

2008-02-28, 15:44   #8
Wacky

Jun 2003
The Texas Hill Country

21018 Posts

Quote:
 Originally Posted by jasonp Does merge level 2 create relation sets out of relations that have ideals of weight 2? The filtering deleted 220k relation sets, could those sets contain a huge number of relations somehow? Also, when does singleton removal happen in this scheme, and can it be responsible for deleting many more relations than ideals? Finally, 25% duplicates sounds like a lot, maybe you needed to do a lot more sieving and the removed duplicates turned many ideals into singletons.
Yes, mergelevel n (n>1) creates sets by merging on ideals that appear no more than n times.

Although duplicate and singleton can be, and often are, done before mergelevel 2, they are also done at each pass at the higher levels.

However, consider the effect of merging on "excess".
In the case of a duplicate, you remove one relation and zero ideals, for a net "cost" of 1.
In the case of a singleton, you remove one relation and one (or more) ideals, for a net "cost" of 0 (or, potentially, a net gain)
In the case of a doubleton, you remove 2 relations, 1 ideal and introduce 1 "set", for a net "cost" of 0 (unless the resulting set is discarded as "heavy" - but that is counted separately.)

Thus, the net effect on excess by doing any level merge should be no worse than the sum of the duplicates eliminated + the "heavy" discards.

2008-02-28, 16:01   #9
R.D. Silverman

Nov 2003

746010 Posts

Quote:
 Originally Posted by Wacky Thus, the net effect on excess by doing any level merge should be no worse than the sum of the duplicates eliminated + the "heavy" discards.
Exactly. Which is why I am puzzled about the disappearing excess.

2009-02-04, 17:47   #10
bdodson

Jun 2005
lehigh.edu

210 Posts

Quote:
 Originally Posted by garo Code: Base Index Size 11M(45digits) 43M(50digits) 110M(55digits) 260M(60digits) Decimal 12 233- C215 12 239- C202 12 241- C260 factored Childers/Dodson/Wackerbarth 12 247- C209 12 257- C269 p52*c218 12 269- C205 12 271- C234 12 277- C285 12 281- C294 12 283- C295 ==> c244 Nakano+Imaishi+Kawashima+Ohno 12 289- C248 12 293- C293 12 295- C228 12 299- C174
New p52 = 3210333482150938236735353240875928231167166319686291
from 12,257- C269, found twice overnight, with B1 = 260M. Cofactor starts
c218 = 23231152219465... Likewise, the c244 cofactor of 12,283- starts
448271923276293... The snfs difficulty for 257- is around 276, so the
c218 is still likely easier by snfs (but somewhat less attractive, as a smaller
number). -Bruce

Last fiddled with by bdodson on 2009-02-04 at 17:52 Reason: credit due, twice

2009-02-04, 18:05   #11
10metreh

Nov 2008

2×33×43 Posts

Quote:
 Originally Posted by bdodson New p52 = 3210333482150938236735353240875928231167166319686291 from 12,257- C269, found twice overnight, with B1 = 260M. Cofactor starts c218 = 23231152219465... Likewise, the c244 cofactor of 12,283- starts 448271923276293... The snfs difficulty for 257- is around 276, so the c218 is still likely easier by snfs (but somewhat less attractive, as a smaller number). -Bruce
How much ECM had been done on that number at lower levels? A P52 seems rather small for a B1 of 260M.

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