The probable primes - Page 26

Cybertronic · 2010-05-25, 20:29

First of all , the latest version is not limited ... I mean , you can test more than 100000 bits. It is enough for a world record.

The power law is d^3,75 and that is very stable.

The next number takes about 18 months on a 3,4 GHz quadcore and have near 17000 digits. The chance is marginal to prove this large numbers.
It was a luck for me. Maybe one point I had have to finished TEST 1, only one ! My gigantic triplet with 10047 digits from 2008 , I can't certified with PRIMO.

More cores than 4 are better. You can TEST more possible ways simultan, also you can calculate Phase 2 parallel.

I don't believe that exist a multicore version of PRIMO...for Marcel is it to
expansiv to rewrite. He told it me one year ago.

"You to be crackers" to beat the actual record..it was very hard for my nerves. You need near 120 days a full time visual contact to the display.
I doubt that PRIMO can certified the actual record alone. Is it so, it takes near 3 years on a Phenom 965.

So, the first 100 bit are done ( at TEST 4 )

enderak · 2010-05-25, 21:00

Thank you for the information. I thought the latest version was still limited to 50K bits. Also, I did not know there was luck involved with proving the large numbers, just time.

philmoore · 2010-05-25, 21:44

My memory may be fallible here, but I do remember Marcel Martin expanding his table of discriminants in one release of Primo. He said that it would increase the size of numbers that could be proven with the program, but that at some point, the program would run in to numbers that it could not certify. My guess is that Francois Morain's FastECCP program plus access to a sizeable cluster of processors could probably do the next four numbers, but I don't believe that his program is publicly available. The record Mills' prime with 20562 digits was proven on a cluster in 2007 after 9 months of work! Of course, computers are faster now...

Too bad that Marcel does not have the time or inclination to write a multi-processor version, but Norman has definitely proven that the concept is a good one. Sooner or later, some programmer will take up the challenge.

mdettweiler · 2010-05-26, 01:51

Quote:

Originally Posted by philmoore

My memory may be fallible here, but I do remember Marcel Martin expanding his table of discriminants in one release of Primo. He said that it would increase the size of numbers that could be proven with the program, but that at some point, the program would run in to numbers that it could not certify. My guess is that Francois Morain's FastECCP program plus access to a sizeable cluster of processors could probably do the next four numbers, but I don't believe that his program is publicly available. The record Mills' prime with 20562 digits was proven on a cluster in 2007 after 9 months of work! Of course, computers are faster now...

Too bad that Marcel does not have the time or inclination to write a multi-processor version, but Norman has definitely proven that the concept is a good one. Sooner or later, some programmer will take up the challenge.

Following links on the Prime Pages' FastECPP entry, I was able to find what appears to be a downloadable FastECPP version here. Might this be what you're looking for?

Also, a quick question since I'm not very familiar with how ECPP works: just how parallelizable can it get? That is, with FastECPP, can it be massively distributed (i.e., split up into work chunks and reserved by a disparate group a la PRP testing or sieving), or does it have to be done within a somewhat-directly-connected cluster?

philmoore · 2010-05-26, 02:20

That version of Francois Morain's ECPP program dates from April 2001 and predates the FastECPP version, I believe.

I expect that "parallel" here means that different processors investigate different paths to try to reduce the complexity of the problem, as measured by the bit length of the current prp for which a primality proof is desired. But the different paths must be compared regularly to see which one is actually making the best progress, so that the less productive paths can be pruned, and new branches can be spun off the more productive paths. So yes, ongoing communication between the various processors is necessary. Some of the papers on Morain's webpage would give more specific details, of course.

Cybertronic · 2010-05-26, 03:06

Quote:

Originally Posted by philmoore

My memory may be fallible here, but I do remember Marcel Martin expanding his table of discriminants in one release of Primo. He said that it would increase the size of numbers that could be proven with the program, but that at some point, the program would run in to numbers that it could not certify.

I have this version ... (8 tables) ,but it was also not usefuly for my 10047 digit number. The MSC-feature in the actual version is much better than the 8 tables,definite!

For the actual record number , Marcel told me : " I'm in an unknown land ! "

The 8 tables version was maybe good for 6000 digits , but at that time nobody will try a 11k digit number and will risk a runtime of factor 40 or more.
For this numbers ,the powerlaw is not 4,5-4,9. It is maybe >6. Well, a 1 GHz Athlon need maybe 15-20 years for my number,alone.

Cybertronic · 2010-06-01, 06:43

Status of 2^28978+34429:

Ph1: TEST 50 (8277/8724 digits)
Ph2: 1-22 done

Elapsed time: 150h

engracio · 2010-06-01, 18:37

Quote:

Originally Posted by Cybertronic

Status of 2^28978+34429:

Ph1: TEST 50 (8277/8724 digits)
Ph2: 1-22 done

Elapsed time: 150h

Wow Norman at your pace, you would probably finish your prime before I finally finish mine. You are blasting away Norman.

Good job.

Cybertronic · 2010-06-02, 04:00

Thanks engracio.

All to go according to plan. Maybe done at 10th July.

What is your status ?

Best,
Norman

engracio · 2010-06-02, 14:44

I am just running AMD 965 4x now and just on test 275 since 14 Feb.

Overall I am happy with the progress. I know I will eventually finish it.

Cybertronic · 2010-06-02, 18:50

Oh, the same maschine like me

.

Your number will have 1230 TESTs total. You have maybe 24500 bits left
and 60% done. In 5-6 weeks you are done.

2010-05-25, 20:29	#276
Cybertronic Jan 2007 Germany 2CD₁₆ Posts	First of all , the latest version is not limited ... I mean , you can test more than 100000 bits. It is enough for a world record. The power law is d^3,75 and that is very stable. The next number takes about 18 months on a 3,4 GHz quadcore and have near 17000 digits. The chance is marginal to prove this large numbers. It was a luck for me. Maybe one point I had have to finished TEST 1, only one ! My gigantic triplet with 10047 digits from 2008 , I can't certified with PRIMO. More cores than 4 are better. You can TEST more possible ways simultan, also you can calculate Phase 2 parallel. I don't believe that exist a multicore version of PRIMO...for Marcel is it to expansiv to rewrite. He told it me one year ago. "You to be crackers" to beat the actual record..it was very hard for my nerves. You need near 120 days a full time visual contact to the display. I doubt that PRIMO can certified the actual record alone. Is it so, it takes near 3 years on a Phenom 965. So, the first 100 bit are done ( at TEST 4 ) Last fiddled with by Cybertronic on 2010-05-25 at 20:59

2010-06-01, 06:43	#282
Cybertronic Jan 2007 Germany 3·239 Posts	Status of 2^28978+34429: Ph1: TEST 50 (8277/8724 digits) Ph2: 1-22 done Elapsed time: 150h Last fiddled with by Cybertronic on 2010-06-01 at 06:45

2010-06-02, 18:50	#286
Cybertronic Jan 2007 Germany 1315₈ Posts	Oh, the same maschine like me . Your number will have 1230 TESTs total. You have maybe 24500 bits left and 60% done. In 5-6 weeks you are done. Last fiddled with by Cybertronic on 2010-06-02 at 18:57

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2010-05-25, 21:00	#277
enderak Feb 2009 3×13 Posts	Thank you for the information. I thought the latest version was still limited to 50K bits. Also, I did not know there was luck involved with proving the large numbers, just time.

2010-05-25, 21:44	#278
philmoore "Phil" Sep 2002 Tracktown, U.S.A. 19×59 Posts	My memory may be fallible here, but I do remember Marcel Martin expanding his table of discriminants in one release of Primo. He said that it would increase the size of numbers that could be proven with the program, but that at some point, the program would run in to numbers that it could not certify. My guess is that Francois Morain's FastECCP program plus access to a sizeable cluster of processors could probably do the next four numbers, but I don't believe that his program is publicly available. The record Mills' prime with 20562 digits was proven on a cluster in 2007 after 9 months of work! Of course, computers are faster now... Too bad that Marcel does not have the time or inclination to write a multi-processor version, but Norman has definitely proven that the concept is a good one. Sooner or later, some programmer will take up the challenge.

2010-05-26, 02:20	#280
philmoore "Phil" Sep 2002 Tracktown, U.S.A. 19·59 Posts	That version of Francois Morain's ECPP program dates from April 2001 and predates the FastECPP version, I believe. I expect that "parallel" here means that different processors investigate different paths to try to reduce the complexity of the problem, as measured by the bit length of the current prp for which a primality proof is desired. But the different paths must be compared regularly to see which one is actually making the best progress, so that the less productive paths can be pruned, and new branches can be spun off the more productive paths. So yes, ongoing communication between the various processors is necessary. Some of the papers on Morain's webpage would give more specific details, of course.

2010-06-02, 04:00	#284
Cybertronic Jan 2007 Germany 3×239 Posts	Thanks engracio. All to go according to plan. Maybe done at 10th July. What is your status ? Best, Norman

2010-06-02, 14:44	#285
engracio May 2007 121₁₀ Posts	I am just running AMD 965 4x now and just on test 275 since 14 Feb. Overall I am happy with the progress. I know I will eventually finish it.