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Old 2016-11-24, 02:24   #12
Batalov
 
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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.
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Old 2016-11-24, 02:31   #13
Dubslow
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If we're going down this road, one could make something of a statement by proving the world's largest illegal prime (and it needn't even be a executable or source code, as Paul has clearly demonstrated ).
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Old 2016-11-28, 01:34   #14
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Thumbs up 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?
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Old 2016-11-28, 07:24   #15
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Quote:
Originally Posted by rudy235 View Post
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
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Old 2016-11-28, 21:19   #16
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Quote:
Originally Posted by paulunderwood View Post


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.
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Old 2017-11-19, 04:35   #17
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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.
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Old 2017-11-19, 05:15   #18
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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?
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Old 2017-11-19, 07:44   #19
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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.
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Old 2017-11-20, 14:49   #20
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Quote:
Originally Posted by mjm View Post
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.
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Old 2020-02-02, 09:47   #21
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Default 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
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Old 2020-02-02, 20:32   #22
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Quote:
Originally Posted by paulunderwood View Post
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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