P16384...
 

This is a thread to exchange benchmarks, curves done and basic info for F[sub]14[/sub]...

I've run these benchmarks on a 2.4GHz AMD64... Attached are the save files so you can play with B2 memory settings and k values...

I'm not sure if I will extend the table any farther... Running B1=43e6 took more than 15 hours...

[code]digits b1 b2 k mem stage 1 ms stage 2 ms

15 2,000 119,805 5 8 2,430 2,608
20 11,000 1,359,460 5 15 13,530 11,881
25 50,000 11,757,135 5 33 61,789 51,133
30 250,000 116,469,998 5 97 310,837 249,851
35 1,000,000 839,549,780 5 249 1,247,434 963,127
40 3,000,000 4,016,636,514 5 544 3,756,443 2,741,624
45 11,000,000 25,577,181,640 20 679 13,831,555 11,372,366
50 43,000,000 54,934,226
55 110,000,000
60 260,000,000
65 850,000,000
70 2,900,000,000[/code]I've most likely made some errors in terminology posting this, so please correct me if you see anything wrong... I'm sure I got the data files made properly, though!

[url]http://mathworld.wolfram.com/FermatNumber.html[/url]

Here is 11e7... This took forever... 218060784ms...

Here are times in seconds for one ECM curve (B2=100*B1) on F14 using Prime95 24.6 on a 2.66GHz P4:
[CODE]
B1 Stage 1 Stage 2

50,000 11 6
250,000 54 25
1,000,000 220 93
3,000,000 661 259
11,000,000 2408 885
43,000,000 9533 3329
[/CODE]

With Prime95 it would be better to run the curves on M32768. Geoff could you time those please?

With Prime95 24.6 it is faster to run individual curves on F12, F13 and F14 than to run a single curve on M32768. Here is the table for a 2.66GHz P4 (with 640Mb allowed for stage two), times are stage1 + stage2 in seconds:

[CODE]
v24.6 v23.8
B1 F12 F13 F14 F12+F13+F14 M32768 M32768

250,000 13+6 25+11 54+25 92+42 112+51 112+50
1,000,000 51+22 99+42 220+93 370+157 445+183 446+184
3,000,000 157+64 295+117 661+259 1113+440 1339+515 1340+515
11,000,000 561+215 1082+401 2408+885 4051+1501 4932+1819 4930+1811

FFT Length 192 384 768 1536
[/CODE]
It is not as simple for other numbers though. For example there is still a significant advantage to running curves on M4132 rather than on M1033, P1033 and P2066 separately. Here is the table for B1=11e6, times in seconds, stage one only:

[CODE]
Number FFT v24.6 v23.8

M1033 48 182 148
P1033 48 184 (not timed)
M2066 96 288 221
P2066 96 301 (not timed)
M4132 192 536 487
[/CODE]
Version 23.8 doesn't report what FFT it is using, the lengths are what version 24.6 reports, maybe they are different?

Thanks for that Geoff. I now vaguely remember reading something about 2^n+1 using some special code as well. But I'm also sure I remember reading something about the size of the numbers in question affecting the M vs. P relative time.

Incidentally, I've been working on M4132 on and off for a bit. I've some 400 unreported curves on all four components.

Factoring F14
 

On Primeform mailing list there is an interesting subject: trying to apply new ECM executables to deepen the search for factors of Fermat numbers (look at their [URL=http://www.mersenne.org/ecmf.htm]actual status[/URL] ), especially F14.

Is there anyone interested in the search?

Luigi

joining the search with 5 computers,
but need a little how-to instruction :-)

cheers, tanya

I am assuming that you are running on computers running some sort of Windows operating system, but if not, feel free to ask questions here.

1) Go to [url]www.mersenne.org[/url] and download the newest version, 24.13. This version offers improvements for Athlon computers as well as dramatic improvements for Pentium-4's.

2) After extracting the files, when Prime95 starts to run, tell it that you are just doing the stress test. Otherwise, it will assume that you want to run test for GIMPS to look for a new Mersenne prime.

3) (Optional, but recommended) Run the stress test for a few hours to make sure that your computers don't have any thermal or memory instabilities that will show up if you start running full time.

4) Go to "Password" on Advanced Menu and enter the password (9876) to turn on the other options in the Advanced Menu. Better yet, look at the readme file first where use of the Advanced Menu is explained.

5) Before starting testing, go to Options and under CPU, set your memory usage to a larger amount, I would think that 64 MBytes should be plenty for F14.

5) In the Advanced Menu, choose "ECM". You will be prompted for the exponent you want. Enter 16384. For stage 1 bound, enter 11000000 (11 million). For stage 2 bound, leave it blank (or 0) and the program will choose 1,100,000,000. For number of curves, try 100 at first. You can always edit the worktodo file later in the Prime95 folder to change the number of curves. Also, check the box that says you want to factor 2^16384 + 1 (rather than 2^16384 -1). Later, if you want, you can run curves to 44000000 for the stage 1 bound.

6) You should be in business. By the way, because no factors are known for P16384 = F14, you do not have to download the lowp.txt file into the Prime95 folder, but if you want to work on numbers with some known factors, you will need either lowp.txt or lowm.txt or both.

7) If you want to use GMP-ECM to run a more efficient stage 2, let us know and I'm sure that someone can point you to a thread that explains how to set that up. If you have a lot of memory, this may be especially worthwhile. But even if you use only Prime95 to do both stages, you will still be making a valuable contribution to the search. F14 has been known to be composite since 1963, so it would truly be historic if a factor shows up. Good luck!

Thank you Phil :smile:

I think a thread for checkouts and results would be nice: this way, I could monthly send results to George to update his Fermat page.

I thought one could work on 2[sup]32768[/sup] - 1 as well: wasn't the "minus" option faster?

Luigi

[quote]I thought one could work on 232768 - 1 as well: wasn't the "minus" option faster?[/quote]

That was until v24. Now, there's no difference in speed...