Any news about Double Mersenne factor search?

biwema · 2008-10-03, 18:16

Is there any news about the double Mersenne factor search?
There are no news on the Will Edgington’s pages for a long time. http://www.garlic.com/~wedgingt/MMPstats.txt

MM13, MM17 and MM19 do not need a lot of coordination. Everyone can run ECM curves and report them to the primenet server.

MM31. Thusfar there are 4 known factors.
The last info I have is that Ernst Mayer is searching up to k=10^15.
That means 82 bit fectors. That is about a 256 times higher k than used for exponent around 33M (68 bit).

Is there any effort to go beyond? Prime95 is quite fast for that task, but difficult to split up the tasks. Maybe it is possible to split up the different passes when editing the factoring save file.
http://www.mersenneforum.org/showpos...86&postcount=7
http://www.mersenneforum.org/showthread.php?t=4229

MM61: Tony Forbes is coordinating a search here.
http://anthony.d.forbes.googlepages.com/mm61prog.htm
Progress: 1bout 1.75*10^15 (Note that N=2k)

MM89, M107: No news known. (k=3.5T; k=2T)

MM127: Erst Mayer searched up to k=2^48 (176 bits).
http://anthony.d.forbes.googlepages.com/mm61prog.htm

Is there any further progress? It would be interesting to add some bits here. There are chances that we finally find a factor ( a bit more then 0.5% per bit). So we finally could stop all these Posts claiming that MM127 is prime…

ET_ · 2008-10-03, 18:46

Quote:

Originally Posted by biwema

Is there any news about the double Mersenne factor search?
There are no news on the Will Edgington’s pages for a long time. http://www.garlic.com/~wedgingt/MMPstats.txt

MM13, MM17 and MM19 do not need a lot of coordination. Everyone can run ECM curves and report them to the primenet server.

MM31. Thusfar there are 4 known factors.
The last info I have is that Ernst Mayer is searching up to k=10^15.
That means 82 bit fectors. That is about a 256 times higher k than used for exponent around 33M (68 bit).

Is there any effort to go beyond? Prime95 is quite fast for that task, but difficult to split up the tasks. Maybe it is possible to split up the different passes when editing the factoring save file.
http://www.mersenneforum.org/showpos...86&postcount=7
http://www.mersenneforum.org/showthread.php?t=4229

MM61: Tony Forbes is coordinating a search here.
http://anthony.d.forbes.googlepages.com/mm61prog.htm
Progress: 1bout 1.75*10^15 (Note that N=2k)

MM89, M107: No news known. (k=3.5T; k=2T)

MM127: Erst Mayer searched up to k=2^48 (176 bits).
http://anthony.d.forbes.googlepages.com/mm61prog.htm

Is there any further progress? It would be interesting to add some bits here. There are chances that we finally find a factor ( a bit more then 0.5% per bit). So we finally could stop all these Posts claiming that MM127 is prime…

I retested some of these ranges with Factor5, that works on MMs in multi-thread mode.

I had the impression that ECM could be more efficient on these ranges, do you think I can be proven wrong?

Luigi

biwema · 2008-10-03, 23:49

Which ranges did you retest?

MM13, MM17 and MM19 are so small that trialfactor won't find any new factor. ECM is the clue here. Prime95, GMP ECM or a combination could be used.

MM31: That number is so large that only trialfactor makes sense. Ernst's application and Prime95 are the most optimized programs. (Use Advanced Factor of the latest 24 Version, it is about 7 times faster than mfac)

MM61, MM89, MM107, MM127 etc.
These are too large for Prime95
I don't know Factor5 and how the performance is compared to Tony Forbes' mfac.

philmoore · 2008-10-04, 04:15

Hopefully, Ernst may respond here. I understood that he was doing some searching on M61, M89, M107, and M127.

Higher iterated Mersennes, odds are low, but who knows? I've wondered about a coordinated search for some time.

ET_ · 2008-10-04, 10:17

Quote:

Originally Posted by biwema

Which ranges did you retest?

MM13, MM17 and MM19 are so small that trialfactor won't find any new factor. ECM is the clue here. Prime95, GMP ECM or a combination could be used.

MM31: That number is so large that only trialfactor makes sense. Ernst's application and Prime95 are the most optimized programs. (Use Advanced Factor of the latest 24 Version, it is about 7 times faster than mfac)

MM61, MM89, MM107, MM127 etc.
These are too large for Prime95
I don't know Factor5 and how the performance is compared to Tony Forbes' mfac.

I partially retested MM31, MM61 and MM127.

I see now how to choose trial-factoring instead of ECM.

Luigi

ET_ · 2008-10-04, 10:18

Quote:

Originally Posted by philmoore

Hopefully, Ernst may respond here. I understood that he was doing some searching on M61, M89, M107, and M127.

Higher iterated Mersennes, odds are low, but who knows? I've wondered about a coordinated search for some time.

I guess the trouble is that there is no real coordination, and the updates are rare and sparse on different pages.

Luigi

biwema · 2008-10-04, 13:34

Quote:

Originally Posted by philmoore

Hopefully, Ernst may respond here. I understood that he was doing some searching on M61, M89, M107, and M127.

Higher iterated Mersennes, odds are low, but who knows? I've wondered about a coordinated search for some time.

I assume you you MM61, MM89 etc.

According to the posts, Ernst did work on MM31 and MM127;
Tony coordinates MM61;

About the other exponents there is no new information since the update of Will's pages.

I am sorry, but the last link in the first post should have been:
http://www.mersenneforum.org/showthr...t=MM127&page=4

jinydu · 2008-10-07, 02:09

Bump.

Please Ernst Mayer?

geoff · 2008-10-09, 23:43

I am also interested in a co-ordinated search for factors of MM61 and higher.

Mark Rodenkirch has extended his gmp-fermat program to work with double Mersenne numbers and I have added some x86_64-specific assembly that makes it faster on MM61,MM89,MM107,MM127.

I will post some Linux executables for testing if Mark is OK with releasing this version of his program. From the little testing I have done it seems to be significantly faster than the 32-bit MFAC executable, but I don't know how it compares to other programs.

rogue · 2008-10-10, 13:38

Quote:

Originally Posted by geoff

I am also interested in a co-ordinated search for factors of MM61 and higher.

Mark Rodenkirch has extended his gmp-fermat program to work with double Mersenne numbers and I have added some x86_64-specific assembly that makes it faster on MM61,MM89,MM107,MM127.

I will post some Linux executables for testing if Mark is OK with releasing this version of his program. From the little testing I have done it seems to be significantly faster than the 32-bit MFAC executable, but I don't know how it compares to other programs.

Go ahead and release the source.

geoff · 2008-10-10, 23:44

gmp-fermat-21.zip contains Linux executables dm32 and dm64 to search for factors of double Mersenne numbers. Only dm64 has the assembler code to speed up MM61-MM127. (fermat32 and fermat64 search for factors of Fermat numbers).

There isn't any documentation in the archive, but to run it just create a file fermat.ini like this one:

kStart=2
kEnd=100000000
nStart=89
nEnd=89
FilterPrimes=50000

This would cause dm64 to search for factors k*(2^n-1)+1 of the double Mersenne number 2^(2^n-1)-1 for k from 2 to 100000000 and n=89. I don't really know what the optimal value for FilterPrimes is, it will default to 500000 if not given.

2008-10-03, 18:16	#1
biwema Mar 2004 17D₁₆ Posts	Any news about Double Mersenne factor search? Is there any news about the double Mersenne factor search? There are no news on the Will Edgington’s pages for a long time. http://www.garlic.com/~wedgingt/MMPstats.txt MM13, MM17 and MM19 do not need a lot of coordination. Everyone can run ECM curves and report them to the primenet server. MM31. Thusfar there are 4 known factors. The last info I have is that Ernst Mayer is searching up to k=10^15. That means 82 bit fectors. That is about a 256 times higher k than used for exponent around 33M (68 bit). Is there any effort to go beyond? Prime95 is quite fast for that task, but difficult to split up the tasks. Maybe it is possible to split up the different passes when editing the factoring save file. http://www.mersenneforum.org/showpos...86&postcount=7 http://www.mersenneforum.org/showthread.php?t=4229 MM61: Tony Forbes is coordinating a search here. http://anthony.d.forbes.googlepages.com/mm61prog.htm Progress: 1bout 1.75*10^15 (Note that N=2k) MM89, M107: No news known. (k=3.5T; k=2T) MM127: Erst Mayer searched up to k=2^48 (176 bits). http://anthony.d.forbes.googlepages.com/mm61prog.htm Is there any further progress? It would be interesting to add some bits here. There are chances that we finally find a factor ( a bit more then 0.5% per bit). So we finally could stop all these Posts claiming that MM127 is prime…

2008-10-07, 02:09	#8
jinydu Dec 2003 Hopefully Near M48 2×3×293 Posts	Bump. Please Ernst Mayer? Last fiddled with by jinydu on 2008-10-07 at 02:10

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2008-10-03, 23:49	#3
biwema Mar 2004 3·127 Posts	Which ranges did you retest? MM13, MM17 and MM19 are so small that trialfactor won't find any new factor. ECM is the clue here. Prime95, GMP ECM or a combination could be used. MM31: That number is so large that only trialfactor makes sense. Ernst's application and Prime95 are the most optimized programs. (Use Advanced Factor of the latest 24 Version, it is about 7 times faster than mfac) MM61, MM89, MM107, MM127 etc. These are too large for Prime95 I don't know Factor5 and how the performance is compared to Tony Forbes' mfac.

2008-10-04, 04:15	#4
philmoore "Phil" Sep 2002 Tracktown, U.S.A. 10001100001₂ Posts	Hopefully, Ernst may respond here. I understood that he was doing some searching on M61, M89, M107, and M127. Higher iterated Mersennes, odds are low, but who knows? I've wondered about a coordinated search for some time.

2008-10-09, 23:43	#9
geoff Mar 2003 New Zealand 13×89 Posts	I am also interested in a co-ordinated search for factors of MM61 and higher. Mark Rodenkirch has extended his gmp-fermat program to work with double Mersenne numbers and I have added some x86_64-specific assembly that makes it faster on MM61,MM89,MM107,MM127. I will post some Linux executables for testing if Mark is OK with releasing this version of his program. From the little testing I have done it seems to be significantly faster than the 32-bit MFAC executable, but I don't know how it compares to other programs.

2008-10-10, 23:44	#11
geoff Mar 2003 New Zealand 13×89 Posts	gmp-fermat-21.zip contains Linux executables dm32 and dm64 to search for factors of double Mersenne numbers. Only dm64 has the assembler code to speed up MM61-MM127. (fermat32 and fermat64 search for factors of Fermat numbers). There isn't any documentation in the archive, but to run it just create a file fermat.ini like this one: kStart=2 kEnd=100000000 nStart=89 nEnd=89 FilterPrimes=50000 This would cause dm64 to search for factors k*(2^n-1)+1 of the double Mersenne number 2^(2^n-1)-1 for k from 2 to 100000000 and n=89. I don't really know what the optimal value for FilterPrimes is, it will default to 500000 if not given.