M1061...

[Xyzzy]

This is just a thread for all of us to post our progress on this number... I don't know if this is an optimal way to report progress but I'm sure someone will let me know if it isn't... I can't think of an easy way to do a web page with results except by accepting emails and manually updating charts and tables... If this is what we need for M1061 and other numbers like it, as well as the ones B. Silverman mentioned, I'm willing to do that... Otherwise we can have a separate thread for each number, or maybe a thread for each range or type of number...

Anyways, I think we have several things we need to accomplish or answer...

1) How do we determine what value to place on the results from different programs... For example, a stage two curve done on mprime might be worth less than one done on GMP-ECM...

2) How can we help new people get this running on their boxes? I can post a walkthrough for mprime and I think for GMP-ECM, but since I have no access to a Windows box, I don't know how to set that up, other than to use the same worktodo.ini file...

3) How often should we report progress and when do we decide to move on to a deeper bit level?

4) Do we just post the curves we have done or do we need to post additional data?

Anyways, this is just an idea... Let me know if it is stupid or not...

PS - Any technical discussion related to this number is highly encouraged and appreciated!

Mike (Xyzzy)

[Xyzzy]

Our starting point:

http://www.mersenne.org/ecmm.htm

[Xyzzy]

I've completed 102 curves with mprime using B1=44000000, B2=4290000000... I'm switching to GMP-ECM for a while so i can learn that program...

[Xyzzy]

The way I ran this in mprime was to make a directory with the mprime executable in it:

mkdir mprime
cd mprime
wget ftp://mersenne.org/gimps/mprime235.tar.gz
tar -zxvf mprime235.tar.gz

I then created three files:

echo "ECM=1061,44000000,0,100,0,0,0,0" > worktodo.ini

This sets up mprime to do 100 curves with 44e6 as the B1...

echo -e "AskedAboutMemory=1\nUsePrimenet=0\nOutputIterations=1000000000" > prime.ini

If you choose a low number for your output iterations, it will scroll off the screen too fast... You may have to experiment with this value...

echo -e "DayMemory=256\nNightMemory=256" > local.ini

Although you will only need around 50MB to run this number... Make sure you leave enough memory for your OS and regular programs to run without paging or swapping... I have 512MB so I can spare 256MB with no problems... YMMV...

I then started the program with:

nohup nice -19 ./mprime -d >> log.txt

You can then view progress by catting or tailing the log.txt file... Even if you stop mprime and restart it, the counter will not start over, unlike GMP-ECM... If you start it over and it is partway through stage two, it will have to redo that stage...

You can keep a terminal open to view the progress in real time with:

tail -f log.txt

Note: If you stop viewing the output that doesn't mean the program has stopped!

If you want to add a line to cron or a startup script to start this automatically when you boot, you can, although the procedure might be different depending on what distro you use...

[marc]

I've done 44 curves on M1061. It's taking approx 55 minutes with GMP-ECM for each stage with B1=44000000 and B2=184367799127. Is this normal for a 1.8GhZ Athlon? Are there any settings I can change which will decrease this?

[Xyzzy]

Once GMP-ECM is installed you can invoke it like this:

( echo "2^1061-1" | bc | tr -d '\\\n'; echo ) | nohup nice -19 ecm -c 100 44e6 >> log.txt &

You can view the log file the same way as I posted above for mprime...

If I have time in the next few days I will post what akruppa sent me about how to compile GMP-ECM from scratch... For now, if you run Debian, and if you are using "testing" or "unstable" you can do this as root:

apt-get install gmp-ecm

There are a few ways to test whether or not GMP-ECM is installed and working... I will try to post those methods in a while...

[Xyzzy]

Originally Posted by marc

Is this normal for a 1.8GhZ Athlon? Are there any settings I can change which will decrease this?

Can you post one curve from your output? Is your CPU an 1800+ or is it really 1.8GHz? What distro are you running and what versions of the software do you have? How much memory do you have free and are you paging? How much memory does ECM take in stage two?

To get CPU speed, type:

cat /proc/cpuinfo | grep MHz

I'm getting about 35 minutes per curve on my 3200+... I don't have any other benchmarks to compare this to, but maybe someone else will post so we can get an idea!

[marc]

[Fri Oct 15 01:28:43 BST 2004]
GMP-ECM 5.0.3 [powered by GMP 4.1.3] [ECM]
Input number is 24707306311927565716857342128774085333197833223161879682238935306082805123046306993647507776054336486228891340858985829027076261887914242781617846672453431386903982455635542158748401823985988322905245077938567513252198179128990807936780194781391547404884040101606295111368825026273254703636026307207764436438929167613951 (320 digits)
Using B1=44000000, B2=184367799127, polynomial Dickson(30), sigma=1289006054
Step 1 took 2112262ms
Step 2 took 2075776ms

It's really 1.8GHz. It uses about 300mb in Stage 2 and I have plenty spare. It's running on gentoo and weirdly enough there is a GMP 4.1.4 ebuild which has just appeared.

Oh and if you run ecm -v then it tells you it recognises the number as 2**1061 - 1 along with lots of building Gs.

[Xyzzy]

Originally Posted by marc

Oh and if you run ecm -v then it tells you it recognises the number as 2**1061 - 1 along with lots of building Gs.

Excellent!

Here is what it says:

Using special division for factor of 2^1061-1

You could compile it yourself... It is pretty much the usual compile job... Plus, you get 3 scripts to test it to make sure it is working... Run these like this:

./test.ecm ecm
./test.pp1 ecm
./test.pm1 ecm

You will need csh or tcsh installed to run these... The last line of the script will tell you if the test was successful...

[marc]

Yep I compiled it and have the scripts and they erm passed. I guess my Athlon is just slow.

[geoff]

Here are a few curve times that will give a guide for what to expect from P4 based machines.

Times are in seconds. The Celeron runs at 2.88GHz, P4 times have been scaled slightly to match. P4 (HT) times are for the average of two hyperthreads. Versions: mprime 23.9, gmp-ecm 5.0.3, libgmp 4.1.4.

             mprime        gmp-ecm
Stage   |  S1     S2  |  S1     S2    S2    S2    S2    S2    S2    S2
B1/B2   | 44e6  4.3e9 | 44e6  4.3e9  11e9  15e9  22e9  45e9  90e9  180e9
--------+-------------+--------------------------------------------------
Celeron | 546    260  | 1629   117    238   281   382   764
P4      | 545    247  | 1625   108    219   259   349   709  1120  1726
P4 (HT) | 472    193  | 1268    90    180   217   292   595

I used Alex Kruppa's rho.gp program to calculate the effective number of
standard curves as 19300*ecmprob(44e6,B2',sqrt(10)*10^49,k*dF^2,poly):

B2                  4.3e9  11e9  15e9  22e9  45e9  90e9 180e9
polynomial            -12   -12   -12   -12   -30   -30   -30
Standard curves      1.08  1.34  1.42  1.53  1.84  2.08  2.34
Daily output (P4)
 mprime               118
 gmp-ecm               54    63    65    67    68*   65    60
 mprime+gmp-ecm       143   152   153*  148   127   108    89

In summary, a stage 2 time of about half the stage one time gives close to the best result.