Lowest Unknown Prime

GuyMacon · 2011-05-04, 15:55

I am interested in expanding the list of he first N primes. In other words finding the smallest prime that hasn't been found already, then searching for the next one. Can I do this with the present software? If not, is there another project that is working on this?

lycorn · 2011-05-04, 22:05

Quote:

Originally Posted by GuyMacon

In other words finding the smallest prime that hasn't been found already,

Wow! That sounds like guessing the lottery numbers. Can you be more clear?

Uncwilly · 2011-05-04, 23:43

If I understand you correctly, it is a trivial thing to do (of sorts). While many list have been calculated for the lowest primes, many of them have been discarded because it is just as easy to recalculate the list.

Prime95 is not the software that you would want to run.
I don't think that there is a co-ordinated project.

science_man_88 · 2011-05-05, 01:24

Code:

v=[2,3];for(x=4,100,for(y=1,#v,if((x%6==1 || x%6==5) && gcd(x,v[y])==1,v=concat(v,x);break(1))))

I see a flaw in one sense ( because it doesn't work as intended). However I don't know enough to realize why it doesn't as it shows the lowest 6n+5 or 6n+1 number that has a greatest common factor of 1 to the primes ( or not primes in this case) already in the list. using that logic any multiples of primes should be eliminated ( I think it's the break in the if that may be causing something if it gets to it).

cheesehead · 2011-05-05, 01:40

Quote:

Originally Posted by GuyMacon

I am interested in expanding the list of he first N primes.

I can understand that desire.

One problem is communication. Where, exactly, is the list of the first N primes, for the largest N? That question may be unanswerable.

One could do some modest survey to determine the list with largest N that one can find in that survey, then proceed to extend it. AFAIK, with modern computers one could extend that list as fast as one could store the results.

But, where to store the results in such a way that anyone else interested could access it themselves? Who'll pay for the storage space, and for how long?

I started to pose this additional question: how would one communicate that list's existence to whoever is interested? But the answer, of course, would be simply to label the data with "This is the list of the first N primes for the largest N of any such list in the world", or something like that, then let all the search engines find and catalog it. So that part's easy.

Except for the nagging suspicion that someone, somewhere, has a larger list, but isn't allowing search engines to index it.

So I guess one would have to call the list "World's largest list of the first N primes that is indexable by search engines".

Quote:

In other words finding the smallest prime that hasn't been found already, then searching for the next one. Can I do this with the present software?

Sure, but the problem is not doing it, but where to start (and storing the results accessibly, remember). What is the "N"?

CRGreathouse · 2011-05-05, 03:48

If you're seriously interested in this project, I recommend reading
http://primes.utm.edu/nthprime/
and doing similarly.

Jens K Andersen · 2011-05-07, 03:20

See http://primes.utm.edu/notes/faq/LongestList.html.
Considering the time to compute primes versus reading them from a disk or over the Internet, there is not much point in storing trillions of primes.

The project at http://www.ieeta.pt/~tos/goldbach.html has computed all primes up to at least 2*10^18, but not stored them. There are 48645161281738535 primes below 2*10^18. Storage keeps getting cheaper but the cost of storing this amount of data would still be considerable, and a complete waste in my opinion.

I don't know who has the largest online collection of primes but it would be a useless curio. Besides, somebody could set up a system to compute primes on the fly when requested, while falsely claiming they were read from a disk. They could be computed faster than transferred over the Internet.

2011-05-04, 15:55	#1
GuyMacon May 2011 Southern California 2 Posts	Lowest Unknown Prime I am interested in expanding the list of he first N primes. In other words finding the smallest prime that hasn't been found already, then searching for the next one. Can I do this with the present software? If not, is there another project that is working on this?

2011-05-05, 01:24	#4
science_man_88 "Forget I exist" Jul 2009 Dumbassville 2⁶·131 Posts	Code: v=[2,3];for(x=4,100,for(y=1,#v,if((x%6==1 \|\| x%6==5) && gcd(x,v[y])==1,v=concat(v,x);break(1)))) I see a flaw in one sense ( because it doesn't work as intended). However I don't know enough to realize why it doesn't as it shows the lowest 6n+5 or 6n+1 number that has a greatest common factor of 1 to the primes ( or not primes in this case) already in the list. using that logic any multiples of primes should be eliminated ( I think it's the break in the if that may be causing something if it gets to it).

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2011-05-04, 23:43	#3
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 2·3·7·233 Posts	If I understand you correctly, it is a trivial thing to do (of sorts). While many list have been calculated for the lowest primes, many of them have been discarded because it is just as easy to recalculate the list. Prime95 is not the software that you would want to run. I don't think that there is a co-ordinated project.

2011-05-05, 03:48	#6
CRGreathouse Aug 2006 3·1,993 Posts	If you're seriously interested in this project, I recommend reading http://primes.utm.edu/nthprime/ and doing similarly.

2011-05-07, 03:20	#7
Jens K Andersen Feb 2006 Denmark 2×5×23 Posts	See http://primes.utm.edu/notes/faq/LongestList.html. Considering the time to compute primes versus reading them from a disk or over the Internet, there is not much point in storing trillions of primes. The project at http://www.ieeta.pt/~tos/goldbach.html has computed all primes up to at least 210^18, but not stored them. There are 48645161281738535 primes below 210^18. Storage keeps getting cheaper but the cost of storing this amount of data would still be considerable, and a complete waste in my opinion. I don't know who has the largest online collection of primes but it would be a useless curio. Besides, somebody could set up a system to compute primes on the fly when requested, while falsely claiming they were read from a disk. They could be computed faster than transferred over the Internet.