mersenneforum.org New ECPP record (currently: 59,798 digits)
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 2016-11-24, 02:24 #12 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 19×232 Posts The next one should be an ASCII-art Mona Lisa with a bit of noise in the bottom right corner... Or a valid midi file with "Der Hölle Rache kocht in meinem Herzen", flattened as a bytestream.
 2016-11-24, 02:31 #13 Dubslow Basketry That Evening!     "Bunslow the Bold" Jun 2011 40
 2016-11-28, 01:34 #14 rudy235     Jun 2015 Vallejo, CA/. 100011110102 Posts WHAT ARE THE REQUIREMENTS FOR A ECPP OF A GIVEN SIZE? First of all congratulations to Paul for this accomplishment. I wonder if the difficulty of proving primality via ECCP depends mainly on the size of the prime or is it that for the same given size and using _only_ ECPP there are primes that are more difficult to prove. Another open question is how far away in time are we from proving the primality of a 45,000 digit number that has no special for and thus needs a general method?
2016-11-28, 07:24   #15
paulunderwood

Sep 2002
Database er0rr

118616 Posts

Quote:
 Originally Posted by rudy235 First of all congratulations to Paul for this accomplishment.
Thanks very much

Quote:
 I wonder if the difficulty of proving primality via ECCP depends mainly on the size of the prime or is it that for the same given size and using _only_ ECPP there are primes that are more difficult to prove.
There is no difficult prime to prove using ECPP. It depends on the size -- it is an O(log(N)^(4+eps)) algorithm. meaning if you double the length it takes 16 times as long (using the same hardware).

Quote:
 Another open question is how far away in time are we from proving the primality of a 45,000 digit number that has no special for and thus needs a general method?
At the moment Primo is limited to ~35k digits and AFAIK 48 cores. Using the same hardware and techniques as I used, in theory, to get a 45k digit proof would take 14*(45/34)^4 months i.e. 43 months.

Last fiddled with by paulunderwood on 2016-11-28 at 07:43

2016-11-28, 21:19   #16
rudy235

Jun 2015
Vallejo, CA/.

47A16 Posts

Quote:
 Originally Posted by paulunderwood At the moment Primo is limited to ~35k digits and AFAIK 48 cores. Using the same hardware and techniques as I used, in theory, to get a 45k digit proof would take 14*(45/34)^4 months i.e. 43 months.

Thanks. Lets hope that in 43 months (Moore's Law and everything) we can start trying. As an exmple in a month short of 2 years we have managed an increase of ≈ 15% in the number of digits so we could estimate that 6 years from now we can see something like that.

 2017-11-19, 04:35 #17 mjm   May 2012 23 Posts 34987 decimal digits! Yesterday, Peter Kaiser sent me a Primo certificate proving that 2^116224 -15905 is prime. It is a new Primo record, a new ECPP record and a new "ordinary prime" record. Congratulations.
 2017-11-19, 05:15 #18 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 233410 Posts Contraptions on the new record. What is the reason primo or its algo is not utilized through distributed computing? Wouldn't that make new record, regular-primes essentially a daily occurrence?
 2017-11-19, 07:44 #19 yoyo     Oct 2006 Berlin, Germany 659 Posts The main reason is, that primo is a grphical user interface application. A command line version doesn't exists (at least it was the case some years back). In the past I asked the author if a command line version can be provided to include it into a distributed computing project, but he rejected.
2017-11-20, 14:49   #20
paulunderwood

Sep 2002
Database er0rr

118616 Posts

Quote:
 Originally Posted by mjm Yesterday, Peter Kaiser sent me a Primo certificate proving that 2^116224 -15905 is prime. It is a new Primo record, a new ECPP record and a new "ordinary prime" record. Congratulations.

Seconded.A great achievement for Peter, at the cutting edge of what can be done currently.

 2020-02-02, 09:47 #21 paulunderwood     Sep 2002 Database er0rr 2×2,243 Posts 40,000 digits I have just certified the partitions number p(1289844341) which has 40,000 digits. It took 21.5 months on a 4x 12 core AMD 6174. Thanks to Marcel for his impeccable software Last fiddled with by paulunderwood on 2020-02-02 at 10:23
2020-02-02, 20:32   #22
rudy235

Jun 2015
Vallejo, CA/.

2×3×191 Posts

Quote:
 Originally Posted by paulunderwood I have just certified the partitions number p(1289844341) which has 40,000 digits. It took 21.5 months on a 4x 12 core AMD 6174. Thanks to Marcel for his impeccable software
Congratulations! This is clearly a new record and very close to what is achievable with the present software, which I believe is ~ 2132928 ~ 1040015

Last fiddled with by rudy235 on 2020-02-02 at 20:40

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