2^821-1
 

This is the [i]mersenne[/i]forum factoring forum, and we're demonstrably able to do quite large SNFS jobs, so I've reserved the smallest unfactored Mersenne number.

I'm afraid this will be perhaps 30% more work than 3^512+1 was; the SNFS difficulty is only three digits more, but the yield of relations does not seem as good. As for 3^512+1, use gnfs-lasieve4I15e.

[code]
n: 1061244591507170837476394518295406773413033058567971362754037707602701554995003142600106989606370443665400533464086399877589805021812659427420956337676840056998663356824134600362050233184172947122074652274833
skew: 1
c6: 1
c0: -2
Y1: -1
Y0: 174224571863520493293247799005065324265472
lpbr: 31
lpba: 31
mfbr: 62
mfba: 62
rlambda: 2.6
alambda: 2.6
rlim: 80000000
alim: 100000000
[/code]

For this polynomial both rational and algebraic special-Q make sense (gnfs-lasieve4I15e -a or -r); if you're searching below Q=100 million, and that's where I'd recommend sieving, some versions of gnfs-lasieve will complain that Q is less than the rlim or alim value; reduce that value to equal the smallest Q.

One side for a range of a million around Q=10^8 will take about eight days on one Core2/2400 core, and produce about 2.4 million relations, so my estimate is that we'll need 40 to 50 MQ, sieved on both sides. Make reservations in the 40M-100M range, and probably we'll have a respectable matrix before the range is fully covered.

[b]28/5[/b] Don't bother reserving in the 60-70 range; if we've filled 40-60 and 70-100, there will be way more than enough relations, and your computrons are best directed elsewhere

[b]Reservations[/b][code]
* andi47 40-41 R
**Anonymous 40-40.5 A 1417387
**fivemack 40.5-41A 1451939
SMH 41-45 A+R
(** 41-42 2887442A + 3179858R)
(** 42-43 2898467A + 3173150R)
(** 43-44 2871097A + 3148816R)
(** 44-45 2850341A + 3140860R)
** Anonymous 45-45.5 1575277R
* SMH 46-48 A+R
(** 46-47 2830314A)
(** 46-48 final group 4101765 total)
fivemack 48-60 A+R
(** 48-49 2807006A + 3075952R)
(** 49-50 2823541A + 3079696R)
(** 50-51 2964737A + 2878872R)
(** 51-52 2784766A + 3047309R)
(** 52-53 2755609A + 3026947R)
(** 53-54 2861528A + 2931863R)
(** 54-55 2721184A + 2998539R)
(** 55-56 2931885A + 2819319R)
(** 56-57 2909069A + 2815967R)
(** 57-58 2887275A + 2792191R)
(** 58-59 2708219A + 2968525R)
(** 59-60 2842829A + 2772860R)
**bdodson 70-100 A+R
(70- 80A 25430044)
(80- 90A 24789184)
(90-100A 24207823)
(70- 80R 27902110)
(80- 90R 26703849)
(90-100R 25559742)
**fivemack 100-101 2461307A+2417030R
[/code]

[code]
21/05/2008 21:23 110519789 relations; 102720875 unique; about 82378835 large ideals
24/05/2008 12:11 174262339 relations; 154245428 unique; about 91053621 large ideals
matrix is 14624280 x 14624528 (4005.8 MB) with weight 987631043 (67.53/col)
sparse part has weight 903858759 (61.80/col)
memory use 3962.7MB, estimated runtime (1 CPU) = 1230 hours, 51 days, 4-CPU estimate 30d
30/05/2008 08:37 200863237 relations; 172478095 unique; about 93018231 large ideals
matrix is 12152185 x 12152433 (3284.7 MB) with weight 808859623 (66.56/col)
sparse part has weight 739549610 (60.86/col)
memory use 3249.8MB, estimated runtime (1 CPU) = 794 hours (33 days), 4-CPU estimate 20d
07/06/2008 12:30 266645965 relations; 214596314 unique; about 96357373 large ideals
matrix is 10129794 x 10130042 (2798.1 MB) with weight 690519820 (68.17/col)
sparse part has weight 632200045 (62.41/col)
memory use 2989.1MB, estimated runtime (4 CPUs) = 379 hours (15.8 days)
[/code]

[QUOTE=fivemack;133105]This is the [i]mersenne[/i]forum factoring forum, and we're demonstrably able to do quite large SNFS jobs, so I've reserved the smallest unfactored Mersenne number.

I'm afraid this will be perhaps 30% more work than 3^512+1 was; the SNFS difficulty is only three digits more, but the yield of relations does not seem as good. As for 3^512+1, use gnfs-lasieve4I15e.

...

For this polynomial both rational and algebraic special-Q make sense (gnfs-lasieve4I15e -a or -r); you'll have to reduce one or the other limit if you're searching below Q=100 million.

[b]Reservations[/b]
fivemack 100-101 A+R[/QUOTE]

I'd be willing to take a 30M range on the R-side, if you don't mind
my using a slightly different version of Greg's binary:

[code]
-rwxr-xr-x ... 1129598 Apr 1 06:14 gnfs-10mo-lasieve4I15e
-rwxr-xr-x ... 1128456 Mar 28 19:54 gnfs-lasieve4I15e [/code]

where the March 28 version was what I used for the last of my 512+
relations. Among other changes, this version allows sieving by qs below
the factor base bound (so I wouldn't need to adjust/reduce the limit.
actually, the "one or the other" instruction may be a bit elliptical for
those with standard binaries, I'm not sure myself what is intended. Aren't
almost all of the qs on the R-side, and many/most of the qs on the A-side
under the factorbase limit(s)? sorry for the quibble.).

Do I correctly gather that there isn't a block of width 30M above 100M
(as 512 only ran up to 125M, and this one has both R and A, so the
max would be no larger than 125M?). If that's correct, and the binary
is OK, I'd take 70M-100M on the R-side. No special Lehigh/NFSNET
acknowledgement needed; this would be a toll-free mersenne number
contribution. The 30M would take under 24 hours here (unless other
users show up), and would (hopefully) give some useful sieving without
adding to my diskspace crises.

On that topic (if you don't mind), does msieve actually need
msieve.dat during all of the lanczos job? For example, with -nc2
and/or -ncr (so that msieve wouldn't directly head into the sqrt),
and a full week or more of lanczos left to run, would files including

[code]
-rw-r--r-- ... 446037712 May 12 08:24 msieve.dat.chk
-rw-r--r-- ... 304200968 Apr 25 04:33 msieve.dat.cyc
-rw-r--r-- ... 3740484004 Apr 25 04:34 msieve.dat.mat
-rw-r--r-- ... 429158932 Apr 25 01:14 msieve.dat.s [/code]
but not msieve.dat suffice? If so, I'd keep it on a different
disk (and be able to run all four matrices in /home, which is
faster than /vtmp).

Along the same line, I'm wondering what would be needed to be
saved to another disk to be able to pause or save an msieve computation
for, say, a week or two; perhaps while continuing to run msieve/lanczos.
Looks like only the chk files are being written, so keeping all of the above,
along with the initialization files (work.. .fb) and msieve.dat should
suffice? For example, suppose I were inattentive when restarting after
a system reboot (or crash), and hit -nc2 instead of -ncr. Without a
complete backup of all of the above, I believe I've seen msieve.dat.mat
over-written, after which an older saved .chk might be useless(?).

Apollogies for the muttering and mumbling; I'm looking forward
to having womack/mersenneforum finish this first-hole on the
Cunningham base-2 lists cleared. -Bruce

(ps - I heard a rumor that a certain 18M^2 msieve matrix has finished; and
that the smallest factor isn't quite small enough to be considered
an ecm miss.)

70-100M on the R side would be fantastic, thanks! The precise version of the lasieve binary is I think immaterial.

Yes, most of the Q I'm looking at are below the factor base bound.

As far as I know the msieve.dat file is not needed during the Lanczos stage; at least, -ncr restarts sufficiently quickly that I'd be rather surprised if it were doing anything with msieve.dat. I would be tempted just to copy files into a temp directory until msieve -ncr starts to work in that directory; the Lanczos stage accesses the disc only to write checkpoints.

[QUOTE=bdodson;133264]
On that topic (if you don't mind), does msieve actually need
msieve.dat during all of the lanczos job? For example, with -nc2
and/or -ncr (so that msieve wouldn't directly head into the sqrt),
and a full week or more of lanczos left to run, would files including

[code]
-rw-r--r-- ... 446037712 May 12 08:24 msieve.dat.chk
-rw-r--r-- ... 304200968 Apr 25 04:33 msieve.dat.cyc
-rw-r--r-- ... 3740484004 Apr 25 04:34 msieve.dat.mat
-rw-r--r-- ... 429158932 Apr 25 01:14 msieve.dat.s [/code]
but not msieve.dat suffice? If so, I'd keep it on a different
disk (and be able to run all four matrices in /home, which is
faster than /vtmp).
[/QUOTE]
Once the matrix is built, only the .chk and .mat files are needed to restart a paused matrix solve. You are correct that running -nc2 a second time is not guaranteed to generate the same matrix file, and if it does not then an old checkpoint file will not be able to restart properly. You still need to restart with '-s <dat_file_name>' because this provides the filename prefix to use, but the .dat file itself should not be needed.

The filtering requires only the .dat file, the linear algebra requires the .dat and .cyc files to generate the matrix, restarting the linear algebra requires only the .mat and .chk files, and the square root requires the .dat, .cyc, and the .dep file that is the output from the LA.
[QUOTE]
(ps - I heard a rumor that a certain 18M^2 msieve matrix has finished; and
that the smallest factor isn't quite small enough to be considered
an ecm miss.)[/QUOTE]
So coy, sheesh :)

Do you have a place to upload the relations?

What file name format should i use?

Please use names like 2-821.41M-42M.r.gz or 2-821.70M-80M.a.gz, and upload the relations by

[code]
ftp chiark.greenend.org.uk
user anonymous, password {your email address}
cd special/twomack-relations/aarhus
binary
put 2-821.41M-42M.r.gz
[/code]

There ought to be plenty of room on the drive, and there will be even more when I've finished factoring 3^512+1 and stop feeling I need to keep offsite backups of the relations.

I'm interested in helping out here a little bit, but can't get gnfs-lasieve to build on 32-bit Linux (I'm not very experienced in the area of compiling software from source). Can somebody please point me in the general direction of gnfs-lasieveI14e or gnfs-lasieveI15e compiled for 32-bit Linux?

If that doesn't pan out, I can always use the precompiled Windows version through Wine (since Wine usually doesn't have much of an impact, if any, on apps such as this), though that's a bit of a messy workaround and I'd rather avoid it if possible. :smile:

Thanks in advance! :smile:

Well, I just ran a benchmark (using the info provided in the M2376 parameters thread) with gnfs-lasieve4I14e.exe through Wine on my system (Core 2 Duo 2.2Ghz running Ubuntu 32-bit), and the benchmark timings looked competitive, so I think running it through Wine will do just fine. :smile: Of course, it would still be optimal to use a native Linux binary, so any pointers on where to get that are still welcome. :smile:

I'll reserve 40-41 on the A side to get acquainted with how long these things will take on my CPU. :smile:

Oh, BTW, I forgot to ask this: if I need to stop gnfs-lasieve4I14.exe for whatever reason, how do I make it pick up where if left off when I restart?

See [url]http://www.mersenneforum.org/showthread.php?t=9772:[/url]

'If your computer crashes mid-job, look at the last hex number on the last full line of the output file '55.56', convert it to decimal, and use that as the '-f' when you start again; subtract from '-c' appropriately so that your range ends in the right place.'

Though if you're sieving on the rational side (which you're not, at least this time), it's the last hex number [i]before the colon in the middle[/i] that you need:

[code]
12571943595,90442:da66c29,17455,55543,7,2B,47,3,3,B,B,2625A01:11c54b27,84f9ac1,2A2D7,34565,67553,12B7B9,19CF,148D,5,5,1F,1F3,2,2
^^^^^^^ this one
[/code]

[quote=fivemack;133418]See [URL]http://www.mersenneforum.org/showthread.php?t=9772:[/URL]

'If your computer crashes mid-job, look at the last hex number on the last full line of the output file '55.56', convert it to decimal, and use that as the '-f' when you start again; subtract from '-c' appropriately so that your range ends in the right place.'

Though if you're sieving on the rational side (which you're not, at least this time), it's the last hex number [I]before the colon in the middle[/I] that you need:

[code]
12571943595,90442:da66c29,17455,55543,7,2B,47,3,3,B,B,2625A01:11c54b27,84f9ac1,2A2D7,34565,67553,12B7B9,19CF,148D,5,5,1F,1F3,2,2
^^^^^^^ this one
[/code][/quote]
Okay, that makes sense. Just to make sure I've got this straight, given the following line (the last line in my relations file as of ~half a minute ago):
[code]-22979519,7835560:5682ccd3,28DB,30BF,2DBF3,4D44D,4E36D3,B3DAC9,11,C1,265:6462dc37,30545ad9,5C39,6D3F,9D61,18A91,26261F9[/code]
....I'm assuming the number I'd be looking for would be 26261F9, which, converted to decimal, would be 40002041 (which was roughly the q value that it was at at the time)?

Then, I'm also assuming I'd have to specify a new output file when I restart, or else it would overwrite the original relations file (I know because I tried it when I was only a few minutes into the range and didn't have much work to lose)--then I'd just concatenate all the relations files when the range is done, gzip them up, and upload them?