需要大约40m以上的relations（因为会有很多冲突）， 贴一个成功的log， 请参看：

Tue Aug 17 10:41:51 2010  begin with 44579074 relations and 39861287 unique ideals
Tue Aug 17 10:42:17 2010  reduce to 24170016 relations and 16859825 ideals in 16 passes

Tue Aug 17 10:12:00 2010  
Tue Aug 17 10:12:00 2010  
Tue Aug 17 10:12:00 2010  Msieve v. 1.45
Tue Aug 17 10:12:00 2010  random seeds: d66a9180 e33300fc
Tue Aug 17 10:12:00 2010  factoring 8191869101213257702214782028182612150271480980815795020417711429874405709482398679692592313772199651759234395055812164164720152614507221054169965684557701 (154 digits)
Tue Aug 17 10:12:02 2010  searching for 15-digit factors
Tue Aug 17 10:12:03 2010  commencing number field sieve (154-digit input)
Tue Aug 17 10:12:03 2010  R0: -249079542923257903468343637582
Tue Aug 17 10:12:03 2010  R1:  1198934780663474129
Tue Aug 17 10:12:03 2010  A0:  264758371267225419757475210394538415
Tue Aug 17 10:12:03 2010  A1: -2055537990492954367224968244085
Tue Aug 17 10:12:03 2010  A2: -7272063811499361094912163
Tue Aug 17 10:12:03 2010  A3:  65264162462209359661
Tue Aug 17 10:12:03 2010  A4:  28881354031644
Tue Aug 17 10:12:03 2010  A5:  8544480
Tue Aug 17 10:12:03 2010  skew 518389.27, size 4.459175e-015, alpha -6.775165, combined = 2.631629e-012
Tue Aug 17 10:12:03 2010  
Tue Aug 17 10:12:03 2010  commencing relation filtering
Tue Aug 17 10:12:03 2010  estimated available RAM is 4096.0 MB
Tue Aug 17 10:12:03 2010  commencing duplicate removal, pass 1
Tue Aug 17 10:12:18 2010  error -6 reading relation 1084441
Tue Aug 17 10:12:34 2010  error -1 reading relation 2155664
Tue Aug 17 10:12:51 2010  error -15 reading relation 3323010
Tue Aug 17 10:13:08 2010  error -15 reading relation 4482267
Tue Aug 17 10:13:29 2010  error -15 reading relation 5657881
Tue Aug 17 10:13:52 2010  error -15 reading relation 6782607
Tue Aug 17 10:14:10 2010  error -15 reading relation 7962913
Tue Aug 17 10:14:10 2010  error -15 reading relation 7966337
Tue Aug 17 10:14:26 2010  error -9 reading relation 9096566
Tue Aug 17 10:15:15 2010  error -1 reading relation 12457318
Tue Aug 17 10:15:47 2010  error -15 reading relation 14636326
Tue Aug 17 10:16:03 2010  error -15 reading relation 15716583
Tue Aug 17 10:16:47 2010  error -11 reading relation 18740465
Tue Aug 17 10:16:58 2010  error -5 reading relation 19503499
Tue Aug 17 10:17:30 2010  error -9 reading relation 21704427
Tue Aug 17 10:19:03 2010  error -15 reading relation 28233616
Tue Aug 17 10:19:27 2010  error -9 reading relation 29916239
Tue Aug 17 10:19:30 2010  error -15 reading relation 30131728
Tue Aug 17 10:19:43 2010  error -5 reading relation 31019559
Tue Aug 17 10:20:10 2010  error -15 reading relation 32829858
Tue Aug 17 10:20:10 2010  error -9 reading relation 32830013
Tue Aug 17 10:20:10 2010  error -5 reading relation 32831184
Tue Aug 17 10:21:52 2010  error -15 reading relation 39859996
Tue Aug 17 10:22:04 2010  error -1 reading relation 40747920
Tue Aug 17 10:22:11 2010  error -9 reading relation 41200025
Tue Aug 17 10:22:43 2010  error -15 reading relation 43400435
Tue Aug 17 10:23:02 2010  error -9 reading relation 44702702
Tue Aug 17 10:23:45 2010  error -15 reading relation 47697744
Tue Aug 17 10:25:06 2010  error -9 reading relation 53221125
Tue Aug 17 10:25:18 2010  error -15 reading relation 54062461
Tue Aug 17 10:25:22 2010  error -11 reading relation 54338176
Tue Aug 17 10:25:44 2010  error -15 reading relation 55834686
Tue Aug 17 10:25:44 2010  found 11352987 hash collisions in 55854595 relations
Tue Aug 17 10:27:28 2010  added 121778 free relations
Tue Aug 17 10:27:28 2010  commencing duplicate removal, pass 2
Tue Aug 17 10:29:31 2010  found 11397298 duplicates and 44579075 unique relations
Tue Aug 17 10:29:31 2010  memory use: 330.4 MB
Tue Aug 17 10:29:31 2010  reading ideals above 44236800
Tue Aug 17 10:29:31 2010  commencing singleton removal, initial pass
Tue Aug 17 10:41:24 2010  memory use: 753.0 MB
Tue Aug 17 10:41:25 2010  reading all ideals from disk
Tue Aug 17 10:41:46 2010  memory use: 766.8 MB
Tue Aug 17 10:41:49 2010  commencing in-memory singleton removal
Tue Aug 17 10:41:51 2010  begin with 44579074 relations and 39861287 unique ideals
Tue Aug 17 10:42:17 2010  reduce to 24170016 relations and 16859825 ideals in 16 passes
Tue Aug 17 10:42:17 2010  max relations containing the same ideal: 32
Tue Aug 17 10:42:21 2010  reading ideals above 720000
Tue Aug 17 10:42:21 2010  commencing singleton removal, initial pass
Tue Aug 17 10:50:08 2010  memory use: 689.0 MB
Tue Aug 17 10:50:08 2010  reading all ideals from disk
Tue Aug 17 10:50:33 2010  memory use: 860.2 MB
Tue Aug 17 10:50:36 2010  keeping 22061209 ideals with weight <= 200, target excess is 140714
Tue Aug 17 10:50:40 2010  commencing in-memory singleton removal
Tue Aug 17 10:50:43 2010  begin with 24170029 relations and 22061209 unique ideals
Tue Aug 17 10:51:14 2010  reduce to 24080746 relations and 21971836 ideals in 10 passes
Tue Aug 17 10:51:14 2010  max relations containing the same ideal: 200
Tue Aug 17 10:51:31 2010  removing 2880449 relations and 2480449 ideals in 400000 cliques
Tue Aug 17 10:51:33 2010  commencing in-memory singleton removal
Tue Aug 17 10:51:36 2010  begin with 21200297 relations and 21971836 unique ideals
Tue Aug 17 10:52:00 2010  reduce to 20985158 relations and 19271837 ideals in 9 passes
Tue Aug 17 10:52:00 2010  max relations containing the same ideal: 189
Tue Aug 17 10:52:16 2010  removing 2136561 relations and 1736561 ideals in 400000 cliques
Tue Aug 17 10:52:17 2010  commencing in-memory singleton removal
Tue Aug 17 10:52:20 2010  begin with 18848597 relations and 19271837 unique ideals
Tue Aug 17 10:52:39 2010  reduce to 18705638 relations and 17389712 ideals in 8 passes
Tue Aug 17 10:52:39 2010  max relations containing the same ideal: 174
Tue Aug 17 10:52:53 2010  removing 1901118 relations and 1501118 ideals in 400000 cliques
Tue Aug 17 10:52:54 2010  commencing in-memory singleton removal
Tue Aug 17 10:52:56 2010  begin with 16804520 relations and 17389712 unique ideals
Tue Aug 17 10:53:11 2010  reduce to 16675632 relations and 15757256 ideals in 7 passes
Tue Aug 17 10:53:11 2010  max relations containing the same ideal: 163
Tue Aug 17 10:53:23 2010  removing 1775670 relations and 1375670 ideals in 400000 cliques
Tue Aug 17 10:53:24 2010  commencing in-memory singleton removal
Tue Aug 17 10:53:26 2010  begin with 14899962 relations and 15757256 unique ideals
Tue Aug 17 10:53:41 2010  reduce to 14771115 relations and 14249990 ideals in 8 passes
Tue Aug 17 10:53:41 2010  max relations containing the same ideal: 148
Tue Aug 17 10:53:52 2010  removing 1547623 relations and 1189727 ideals in 357896 cliques
Tue Aug 17 10:53:53 2010  commencing in-memory singleton removal
Tue Aug 17 10:53:55 2010  begin with 13223492 relations and 14249990 unique ideals
Tue Aug 17 10:54:07 2010  reduce to 13113622 relations and 12948140 ideals in 8 passes
Tue Aug 17 10:54:07 2010  max relations containing the same ideal: 138
Tue Aug 17 10:54:23 2010  relations with 0 large ideals: 488
Tue Aug 17 10:54:23 2010  relations with 1 large ideals: 480
Tue Aug 17 10:54:23 2010  relations with 2 large ideals: 8212
Tue Aug 17 10:54:23 2010  relations with 3 large ideals: 80424
Tue Aug 17 10:54:23 2010  relations with 4 large ideals: 433732
Tue Aug 17 10:54:23 2010  relations with 5 large ideals: 1399332
Tue Aug 17 10:54:23 2010  relations with 6 large ideals: 2854210
Tue Aug 17 10:54:23 2010  relations with 7+ large ideals: 8336744
Tue Aug 17 10:54:23 2010  commencing 2-way merge
Tue Aug 17 10:54:38 2010  reduce to 8572728 relation sets and 8407246 unique ideals
Tue Aug 17 10:54:38 2010  commencing full merge
Tue Aug 17 10:57:54 2010  memory use: 861.8 MB
Tue Aug 17 10:57:56 2010  found 4575403 cycles, need 4551446
Tue Aug 17 10:57:57 2010  weight of 4551446 cycles is about 318690890 (70.02/cycle)
Tue Aug 17 10:57:57 2010  distribution of cycle lengths:
Tue Aug 17 10:57:57 2010  1 relations: 530089
Tue Aug 17 10:57:57 2010  2 relations: 589308
Tue Aug 17 10:57:57 2010  3 relations: 601452
Tue Aug 17 10:57:57 2010  4 relations: 547252
Tue Aug 17 10:57:57 2010  5 relations: 487379
Tue Aug 17 10:57:57 2010  6 relations: 416283
Tue Aug 17 10:57:57 2010  7 relations: 345686
Tue Aug 17 10:57:57 2010  8 relations: 278183
Tue Aug 17 10:57:57 2010  9 relations: 215331
Tue Aug 17 10:57:57 2010  10+ relations: 540483
Tue Aug 17 10:57:57 2010  heaviest cycle: 20 relations
Tue Aug 17 10:57:59 2010  commencing cycle optimization
Tue Aug 17 10:58:08 2010  start with 23670451 relations
Tue Aug 17 10:59:03 2010  pruned 592192 relations
Tue Aug 17 10:59:03 2010  memory use: 625.9 MB
Tue Aug 17 10:59:03 2010  distribution of cycle lengths:
Tue Aug 17 10:59:03 2010  1 relations: 530089
Tue Aug 17 10:59:03 2010  2 relations: 603246
Tue Aug 17 10:59:03 2010  3 relations: 624066
Tue Aug 17 10:59:03 2010  4 relations: 560657
Tue Aug 17 10:59:03 2010  5 relations: 498445
Tue Aug 17 10:59:03 2010  6 relations: 420505
Tue Aug 17 10:59:03 2010  7 relations: 346981
Tue Aug 17 10:59:03 2010  8 relations: 274484
Tue Aug 17 10:59:03 2010  9 relations: 208769
Tue Aug 17 10:59:03 2010  10+ relations: 484204
Tue Aug 17 10:59:03 2010  heaviest cycle: 20 relations
Tue Aug 17 10:59:40 2010  RelProcTime: 2857
Tue Aug 17 10:59:40 2010  elapsed time 00:47:40
Tue Aug 17 10:59:40 2010  
Tue Aug 17 10:59:40 2010  
Tue Aug 17 10:59:40 2010  Msieve v. 1.45
Tue Aug 17 10:59:40 2010  random seeds: e0aca688 977da19c
Tue Aug 17 10:59:40 2010  factoring 8191869101213257702214782028182612150271480980815795020417711429874405709482398679692592313772199651759234395055812164164720152614507221054169965684557701 (154 digits)
Tue Aug 17 10:59:42 2010  searching for 15-digit factors
Tue Aug 17 10:59:43 2010  commencing number field sieve (154-digit input)
Tue Aug 17 10:59:43 2010  R0: -249079542923257903468343637582
Tue Aug 17 10:59:43 2010  R1:  1198934780663474129
Tue Aug 17 10:59:43 2010  A0:  264758371267225419757475210394538415
Tue Aug 17 10:59:43 2010  A1: -2055537990492954367224968244085
Tue Aug 17 10:59:43 2010  A2: -7272063811499361094912163
Tue Aug 17 10:59:43 2010  A3:  65264162462209359661
Tue Aug 17 10:59:43 2010  A4:  28881354031644
Tue Aug 17 10:59:43 2010  A5:  8544480
Tue Aug 17 10:59:43 2010  skew 518389.27, size 4.459175e-015, alpha -6.775165, combined = 2.631629e-012
Tue Aug 17 10:59:43 2010  
Tue Aug 17 10:59:43 2010  commencing linear algebra
Tue Aug 17 10:59:45 2010  read 4551446 cycles
Tue Aug 17 10:59:58 2010  cycles contain 12983050 unique relations
Tue Aug 17 11:03:47 2010  read 12983050 relations
Tue Aug 17 11:04:19 2010  using 20 quadratic characters above 536870298
Tue Aug 17 11:06:13 2010  building initial matrix
Tue Aug 17 11:11:20 2010  memory use: 1607.0 MB
Tue Aug 17 11:11:29 2010  read 4551446 cycles
Tue Aug 17 11:11:41 2010  matrix is 4551269 x 4551446 (1313.1 MB) with weight 433758678 (95.30/col)
Tue Aug 17 11:11:41 2010  sparse part has weight 307811701 (67.63/col)
Tue Aug 17 11:13:00 2010  filtering completed in 2 passes
Tue Aug 17 11:13:02 2010  matrix is 4550022 x 4550199 (1313.0 MB) with weight 433715154 (95.32/col)
Tue Aug 17 11:13:02 2010  sparse part has weight 307802799 (67.65/col)
Tue Aug 17 11:14:06 2010  read 4550199 cycles
Tue Aug 17 11:24:55 2010  matrix is 4550022 x 4550199 (1313.0 MB) with weight 433715154 (95.32/col)
Tue Aug 17 11:24:55 2010  sparse part has weight 307802799 (67.65/col)
Tue Aug 17 11:24:56 2010  saving the first 48 matrix rows for later
Tue Aug 17 11:24:59 2010  matrix is 4549974 x 4550199 (1259.8 MB) with weight 344923486 (75.80/col)
Tue Aug 17 11:24:59 2010  sparse part has weight 302943501 (66.58/col)
Tue Aug 17 11:24:59 2010  matrix includes 64 packed rows
Tue Aug 17 11:24:59 2010  using block size 65536 for processor cache size 8192 kB
Tue Aug 17 11:26:01 2010  commencing Lanczos iteration (8 threads)
Tue Aug 17 11:26:01 2010  memory use: 1552.3 MB
Tue Aug 17 11:26:24 2010  linear algebra at 0.0%, ETA 35h 3m
Wed Aug 18 22:36:47 2010  lanczos halted after 71957 iterations (dim = 4549974)
Wed Aug 18 22:37:35 2010  recovered 33 nontrivial dependencies
Wed Aug 18 22:38:02 2010  BLanczosTime: 128299
Wed Aug 18 22:38:02 2010  elapsed time 35:38:22
Wed Aug 18 22:38:02 2010  
Wed Aug 18 22:38:02 2010  
Wed Aug 18 22:38:02 2010  Msieve v. 1.45
Wed Aug 18 22:38:02 2010  random seeds: 2fe73a10 f91149cd
Wed Aug 18 22:38:02 2010  factoring 8191869101213257702214782028182612150271480980815795020417711429874405709482398679692592313772199651759234395055812164164720152614507221054169965684557701 (154 digits)
Wed Aug 18 22:38:04 2010  searching for 15-digit factors
Wed Aug 18 22:38:05 2010  commencing number field sieve (154-digit input)
Wed Aug 18 22:38:05 2010  R0: -249079542923257903468343637582
Wed Aug 18 22:38:05 2010  R1:  1198934780663474129
Wed Aug 18 22:38:05 2010  A0:  264758371267225419757475210394538415
Wed Aug 18 22:38:05 2010  A1: -2055537990492954367224968244085
Wed Aug 18 22:38:05 2010  A2: -7272063811499361094912163
Wed Aug 18 22:38:05 2010  A3:  65264162462209359661
Wed Aug 18 22:38:05 2010  A4:  28881354031644
Wed Aug 18 22:38:05 2010  A5:  8544480
Wed Aug 18 22:38:05 2010  skew 518389.27, size 4.459175e-015, alpha -6.775165, combined = 2.631629e-012
Wed Aug 18 22:38:05 2010  
Wed Aug 18 22:38:05 2010  commencing square root phase
Wed Aug 18 22:38:05 2010  reading relations for dependency 1
Wed Aug 18 22:38:07 2010  read 2274574 cycles
Wed Aug 18 22:38:14 2010  cycles contain 6490360 unique relations
Wed Aug 18 22:40:51 2010  read 6490360 relations
Wed Aug 18 22:41:55 2010  multiplying 6490360 relations
Wed Aug 18 23:33:07 2010  multiply complete, coefficients have about 379.07 million bits
Wed Aug 18 23:33:19 2010  initial square root is modulo 6336311
Thu Aug 19 01:22:04 2010  reading relations for dependency 2
Thu Aug 19 01:22:06 2010  read 2274478 cycles
Thu Aug 19 01:22:12 2010  cycles contain 6489940 unique relations
Thu Aug 19 01:24:49 2010  read 6489940 relations
Thu Aug 19 01:25:53 2010  multiplying 6489940 relations
Thu Aug 19 02:17:07 2010  multiply complete, coefficients have about 379.05 million bits
Thu Aug 19 02:17:18 2010  initial square root is modulo 6330547
Thu Aug 19 04:06:07 2010  sqrtTime: 19682
Thu Aug 19 04:06:07 2010  prp77 factor: 72411587307657685190012970300333056897718862529304585414536106974544325602667
Thu Aug 19 04:06:07 2010  prp78 factor: 113129257426828281432524187580381047997575559435912947226758623539913650449103
Thu Aug 19 04:06:07 2010  elapsed time 05:28:05

我在几年前分解成功过一个，一个4核至强跑了4－5个月

今天分解完成。
以下是输出：

Number: xxxxxx
N=8209836131236623540106248032442393614982637631141339598467747244677911494877848116936777629774248859738700738214196985237506543807286694994580847683477459
( 154 digits)
Divisors found:
r1=xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (pp77)
r2=xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (pp78)
Version: Msieve v. 1.52 (SVN unknown)
Total time: 597.64 hours.
Scaled time: 3269.11 units (timescale=5.470).
Factorization parameters were as follows:
name: xxxxxx
n: 8209836131236623540106248032442393614982637631141339598467747244677911494877848116936777629774248859738700738214196985237506543807286694994580847683477459
skew: 199166.65
# norm 8.44e+020
c5: 142201080
c4: -16521935808806
c3: -23440220280166965376
c2: 443026589979303568385914
c1: 281072793633875356163246319501
c0: 396249652594986763475214033106707
# alpha -5.56
Y1: 1229329558890932543
Y0: -141999366259229466501512242214
# Murphy_E 2.87e-012
# M 7655162944996423658347455237206049170649868936407041231974894943450209738969649044677792525403141678664842721593492660297252621214736775154346210101077500
type: gnfs
rlim: 25700000
alim: 25700000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 25700000/25700000
Large primes per side: 3
Large prime bits: 29/29
Max factor residue bits: 58/58
Sieved algebraic special-q in [12850000, 73850001)
Primes: , ,
Relations: relations
Max relations in full relation-set:
Initial matrix:
Pruned matrix : 5763749 x 5763974
Total sieving time: 576.71 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 20.22 hours.
Time per square root: 0.43 hours.
Prototype def-par.txt line would be:
gnfs,153,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,25700000,25700000,29,29,58,58,2.6,2.6,100000
total time: 597.64 hours.

用了readyu提供的avx版本gnfs-lasieve4I14e.exe，分解速度提高了1倍，达到0.11 sec/rel。
在产生足够的关系式后，msieve 1.52 svn939产生错误，说矩阵不是可逆的。
后来换了一个msieve，最终成功解析矩阵。

提供一下实际分解经验，大概300-400个核（超算平台），2-3天分解一个512的数

ggnfs-svn413-win64-core2  和 msieve152_svn939_win64_i7  今天早上开始分解 1024 的rsa 不知道多久，反正电脑天天开，2年内分解出来，就应该能用上，2年之后的话，就没有意义了，（电脑配置 I5 3210  12G
内存 win7 64 位）  西天取经去了！

gnfs-lasieve4I14e.exe 在哪里下载，最近也需要分解一个154-digit input ,谢谢分享！！！

http://gilchrist.ca/jeff/factoring/index.html

下载前面2个文件。发现第3个文件下载不了。
CYGWIN  或  Brian Gladman's factmsieve.py   这2个的其中一个都下不了。

那个好心人，上传一下这个第3个文件？谢谢了。。

附件含 factmsieve.py 的两个版本：
1) version 0.83
2) use mpi for the Linear Algebra stage of msieve

上传的附件：

• factmsieve.py.rar （38.39kb，170次下载）

谢谢MistHill,下载试试看，

I7 16G内存分解一个154-digit  需要多长时间？

从#4楼的log看，大概是25天。这也只是个参考，具体的分解可能差异较大。
但请注意，楼主用了 readyu 的 AVX 版本，速度提高了1倍！

Intel Core i7/i5/i3 的 Sandy Bridge (E)， Ivy Bridge (E)， Haswell (E)，Broadwell (E) 支持 AVX 扩展。
Haswell (E)，Broadwell (E) 还支持 AVX2。

@MistHill readyu 的 AVX 版本这个版本哪里可以下载到

猜想是 readyu 编译的，可向 readyu 或楼主寻求帮助；也可尝试自己编译。

你所说的应该是yafu-1.34 这个版本的吧  但是具体怎么用不会...

看帖仔细一点。

用了readyu提供的avx版本gnfs-lasieve4I14e.exe，分解速度提高了1倍，达到0.11 sec/rel。

你分解RSA512的时候 第一步用了多长时间？

出现这个问题是哪里的问题 求解

-> This is client 1 of 1
-> Running on 6 Cores with 6 hyper-threads per Core
-> Working with NAME = example
-> Selected default factorization parameters for 154 digit level.
-> Selected lattice siever: gnfs-lasieve4I14e
-> Creating param file to detect parameter changes...
-> Running setup ...
-> Estimated minimum relations needed: 5.70292e+07
-> cleaning up before a restart
-> Running lattice siever ...
-> entering sieving loop
-> Running matrix solving step ...
-> msieve -s example\example.dat -l example\example.log -i example\example.ini -
nf example\example.fb -t 36 -nc2
Return value 4294967295. Terminating...

C:\ggnfs\example>

我去年用一台16核（超线程32核）至强E7处理器的服务器，31个核跑，6天解了一个rsa512。

http://173.254.28.24/~brgladma/oldsite/computing/factoring.php

我倒，如果放到国家的天河，1024都是个渣了，看样子已经没什么安全的东西了

不知可否写一个 详细的过程，造福后来者~

保存，留着慢慢学习

由readyu提供。

上传的附件：

• gnfs-lasieve4I14e-x64-AVX.rar （238.91kb，285次下载）