2+ table

[fivemack]

Sieved 2^860+1 for Q=42M..60M on the rational side using 15e (which took about 9.1 million seconds on eight CPUs for 58.83 million relations, 56.00 million unique; 53.4M relations with 51.1M unique was not enough); 87 hours of msieve, to get

Mon Jan 19 13:47:17 2009  matrix is 5820738 x 5820985 (1669.6 MB) with weight 409551060 (70.36/col)
Mon Jan 19 13:47:17 2009  sparse part has weight 379466405 (65.19/col)
...
Mon Jan 19 13:47:57 2009  commencing Lanczos iteration (4 threads)
Mon Jan 19 13:47:57 2009  memory use: 1783.7 MB
Fri Jan 23 01:45:14 2009  lanczos halted after 92054 iterations (dim = 5820734)
Fri Jan 23 01:45:28 2009  recovered 35 nontrivial dependencies
...
(on the second sqrt)
Fri Jan 23 03:27:31 2009  prp96 factor: 269212888053633266896764094842604470698795516716194332265336979146008021202787273766958767916961
Fri Jan 23 03:27:31 2009  prp102 factor: 138776371236300101144144808595934170948601771886820498689521331389066829344376919032939015490766635921

[akruppa]

Nice split!

Alex

[fivemack]

It may be of some interest that

2^923+1 / lcm(2^13+1,2^71+1) = 434284416496884393040841315444206695459788549436182739707934576370088748201819201184526862364134150497353667 * 25319805183489042487156221096767958835909341111097087668817007887186460231678267872101668787950577618516608938546123875314864353811603524007549633

Distinctly over-sieved (15e, 31-bit large primes, small primes 100M on both sides except when that was greater than the special-Q, Q=20M..120M on rational and algebraic sides) by Bruce Dodson at LeHigh to get 366571321 relations of which 234364054 unique; these were transferred to Tom Womack's machine, on which msieve produced three successively denser matrices over 37 hours and ended up running a 10679669 x 10679917 matrix of sparse weight 743029392 (69.57/col). This took 323 hours on 4 threads on a 2.66GHz Core i7, then five square-root attempts at about 2.2 hours x 1 thread each to get the factors.

[Batalov]

Congratulations to Greg and Bruce who have finished the largest msieve filtering job to date!

Greg Childers wrote:
On behalf of Bruce Dodson and myself, it is with great relief that I announce the factors of 2,908+. This was completed with SNFS using msieve for the post-processing.

Congratulations are due to Greg, the largest msieve filtering job to date, on the number of largest snfs difficulty! A sustained effort on the matrix.
-Bruce

[frmky]

Originally Posted by Batalov

Congratulations to Greg and Bruce who have finished the largest msieve filtering job to date!

Thanks Serge! Hopefully with better selection of parameters, we won't have to do another one that large again. The msieve log for the factorization is attached, zipped per Serge's wishes. And for those wondering, the factors are

prp95 factor: 10278473016169511741674978241147093808758455091738490812210128381632640553809934883069084182177
prp174 factor: 148244867657815410685251025382155445432460875370335602150996589909580097524489073313159227345391307390452247708240254482878830828494841709447508662091300316342847949267849729

[R.D. Silverman]

2,865+ C178 = p79.p99 =

3205853408074298683566650869570798974094347365546830062745393897406012552557721 *
322840049452668076280247037005800758274547345385472479309983070175409126454761698489088892852328531

[bdodson]

Originally Posted by R.D. Silverman

2,865+ C178 = p79.p99 =

3205853408074298683566650869570798974094347365546830062745393897406012552557721 *
322840049452668076280247037005800758274547345385472479309983070175409126454761698489088892852328531

We also note the previous entry (corrected):

2, 869+ c222 1341253968916020371683276849882955285358373356754247287123270630\
77028670312366648778721. p136 Batalov+Dodson snfs

the second of nine projected B+D small numbers being done on
Lehigh's newest hardware; with an "appalling" collection of seven
new first holes set by Serge. -Bruce

[R.D. Silverman]

Originally Posted by bdodson

We also note the previous entry (corrected):

2, 869+ c222 1341253968916020371683276849882955285358373356754247287123270630\
77028670312366648778721. p136 Batalov+Dodson snfs

the second of nine projected B+D small numbers being done on
Lehigh's newest hardware; with an "appalling" collection of seven
new first holes set by Serge. -Bruce

It is so nice to have resources!!!!!

[fivemack]

With Jason's software and the sieving resources available to Bruce, 163-digit GNFS is not a hard problem.

Polynomial search with msieve-1.39 with tweaked sieving parameters (first-stage bound 10^25, second-stage 10^23.3, 'third-stage' (NOT murphy_E) 10^-15.5), for a5=1 to 10^5, done by Tom Womack; about 400 CPU-hours over several CPUs.

Final polynomial was

# Murphy_E: 7.25e-13
n: 1447459931133685689731819733718362624021387285345472868400340917637201997410510401320440776572040952789115382200319441628654673769479260524464580088278559757354113
skew: 43703886.03
Y0: -33835736602487934973914042254201
Y1:  2382364346739881539
c0:  2175967112101260296531455335523267483587000
c1: -914379503205478241926289080385151264
c2:  44710065394246436846906938222
c3:  107170167718966915876
c4: -23244745130903
c5:  32640
lpbr: 30
lpba: 30
mfbr: 60
mfba: 60
rlambda: 2.6
alambda: 2.6
alim: 80000000
rlim: 80000000

Bruce sieved 30M..80M on the algebraic side using 15e to get 135844421 relations; I redid 0.01% of the job in 1.1 hours so assume it took about 11000 CPU-hours. msieve-svn-trunk on my i7/2800 did the rest; highlights:

Mon Aug 31 15:18:16 2009  found 20658831 duplicates and 115307765 unique relations
Mon Aug 31 16:39:48 2009  found 6018220 cycles, need 5942516
Mon Aug 31 16:40:50 2009  RelProcTime: 6025
Mon Aug 31 16:40:50 2009  commencing linear algebra
Mon Aug 31 16:40:51 2009  read 5942516 cycles
Mon Aug 31 16:40:59 2009  cycles contain 15049780 unique relations
Mon Aug 31 16:43:09 2009  read 15049780 relations
Mon Aug 31 16:43:31 2009  using 20 quadratic characters above 1073741288
Mon Aug 31 16:44:48 2009  building initial matrix
Mon Aug 31 16:47:54 2009  memory use: 2161.5 MB
Mon Aug 31 16:47:56 2009  read 5942516 cycles
Mon Aug 31 16:47:59 2009  matrix is 5942338 x 5942516 (1796.9 MB) with weight 567660531 (95.53/col)
Mon Aug 31 16:47:59 2009  sparse part has weight 399736320 (67.27/col)
Mon Aug 31 16:49:02 2009  filtering completed in 2 passes
Mon Aug 31 16:49:03 2009  matrix is 5941976 x 5942154 (1796.9 MB) with weight 567648990 (95.53/col)
Mon Aug 31 16:49:03 2009  sparse part has weight 399734046 (67.27/col)
Mon Aug 31 16:49:17 2009  read 5942154 cycles
Mon Aug 31 16:49:20 2009  matrix is 5941976 x 5942154 (1796.9 MB) with weight 567648990 (95.53/col)
Mon Aug 31 16:49:20 2009  sparse part has weight 399734046 (67.27/col)
Mon Aug 31 16:49:20 2009  saving the first 48 matrix rows for later
Mon Aug 31 16:49:22 2009  matrix is 5941928 x 5942154 (1738.0 MB) with weight 452494190 (76.15/col)
Mon Aug 31 16:49:22 2009  sparse part has weight 396173618 (66.67/col)
Mon Aug 31 16:49:22 2009  matrix includes 64 packed rows
Mon Aug 31 16:49:22 2009  using block size 65536 for processor cache size 8192 kB
Mon Aug 31 16:49:51 2009  commencing Lanczos iteration (4 threads)
Mon Aug 31 16:49:51 2009  memory use: 1853.2 MB
Wed Sep  2 16:53:25 2009  lanczos halted after 93967 iterations (dim = 5941924)
Wed Sep  2 16:53:41 2009  recovered 26 nontrivial dependencies
Wed Sep  2 16:53:41 2009  BLanczosTime: 173571
Wed Sep  2 16:53:41 2009
Wed Sep  2 16:53:41 2009  commencing square root phase
Wed Sep  2 16:53:41 2009  reading relations for dependency 1
Wed Sep  2 16:53:41 2009  read 2972376 cycles
Wed Sep  2 16:53:46 2009  cycles contain 9433105 unique relations
Wed Sep  2 16:55:29 2009  read 9433105 relations
Wed Sep  2 16:56:15 2009  multiplying 7527218 relations
Wed Sep  2 17:34:53 2009  multiply complete, coefficients have about 423.00 million bits
Wed Sep  2 17:34:58 2009  initial square root is modulo 38901461
Wed Sep  2 18:55:06 2009  sqrtTime: 7285
Wed Sep  2 18:55:06 2009  prp80 factor: 27330696325754397702721859056296484944945941783920736872107408951551671859754049
Wed Sep  2 18:55:06 2009  prp83 factor: 52960960594688838859111781933077513079102767102893014841306072260677809408420380737
Wed Sep  2 18:55:06 2009  elapsed time 51:54:42

Note that the nearly-6M matrix took 48 hours; this is a fast CPU for linear algebra, as I suppose it is for most other jobs.

[henryzz]

Originally Posted by fivemack

Note that the nearly-6M matrix took 48 hours; this is a fast CPU for linear algebra, as I suppose it is for most other jobs.

what would be a more normal speed for a core 2 quad?

[fivemack]

A slightly smaller (5.2M) matrix took 70 hours on a core2quad.

I happen to have just done some medium-sized SNFS jobs, resulting in ~4M matrices, one on K10/2500 and one on C2/2400. Rerunning the two matrices on the i7:

5+2.298: 112.6ks on four cores of C2/2400, 65.1ks on four cores of i7

5+4.298: 94.7ks on four cores of K10/2500, 65.2ks on four cores of i7

IE the i7 does the job in 60% of the time that the C2/2400 takes, or 70% of the time the K10/2500 takes.

In neither case was I running anything else on the machines, and on the i7 I used taskset to ensure that each thread of linear algebra got its own core (rather than sharing a hyperthreaded core)