20110504, 15:55  #1 
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?

20110504, 22:05  #2 
"GIMFS"
Sep 2002
Oeiras, Portugal
3·509 Posts 

20110504, 23:43  #3 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
3·13·263 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 coordinated project. 
20110505, 01:24  #4 
"Forget I exist"
Jul 2009
Dumbassville
20C0_{16} 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)))) 
20110505, 01:40  #5  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}·3·641 Posts 
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:


20110505, 03:48  #6 
Aug 2006
5979_{10} Posts 
If you're seriously interested in this project, I recommend reading
http://primes.utm.edu/nthprime/ and doing similarly. 
20110507, 03:20  #7 
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 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. 
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