20031222, 14:30  #1 
3×499 Posts 
Who has a list?
While not completly mersenne related, I was wondering who keeps a list of all known primes. I understand that the list would be way too big to easily distribute, but are there people or organizations that are recognized to have the entire list? I coudn't even find a reference to who might have such a list. Also, does anyone here know of any lists avaliable in the 90 to 100 digit range?
Thanks 
20031222, 17:47  #2 
"Gang aft agley"
Sep 2002
7252_{8} Posts 
In my opinion the best place to look is Prime Pages maintained by Dr Chris Caldwell. The is an extremely good site that is very rewarding to read on many levels. As far as prime lists go this is the page on that site: Lists of Primes at the Prime Pages
In this information is a list of the 5000 largest known primes, a list of small primes and others. In the small prime list are some 110 to 200 digit primes (and many others too) I defer to others here concerning questions about entire complete lists of primes. Last fiddled with by only_human on 20031222 at 17:54 
20031222, 20:41  #3 
∂^{2}ω=0
Sep 2002
República de California
11676_{10} Posts 
Any list of the actual primes below some bound B grows exponentially fast with the number of digits in B (i.e. with log B, where the log is to any base), so such lists are not generally kept, as it is faster to simply generate said primes when needed and only explicitly store the ones that are needed at the moment. We know that the number of primes < B scales as B/ln B (natural log here), so e.g. below 2^32 (rouhgly 10^10) we have nearly 2^28 primes, each of which would need ~4 bytes to store explicitly, for a total of roughly a Gigabyte. There are ~10^98 primes < 10^100, which is vastly more than the number of elemntary particles in the known universe. What people have done along these lines is to actually count the number of primes below some everincreasing bound, to check the accuracy of various asymptotic formulae which approximate the primecount function. At present, the prime count has been exactly enumerated to slightly above 10^20, so 10^100 is a long way off! Remember, actual enumeration requires on the order of as many CPUcycles as primes, and in all of human history there have been just slightly above a mole (6.23...X 10^23) of CPUcycles. Even were this count to double each year, it would take over 300 years to reach 10^100.
Here are some related links from MathWorld: http://mathworld.wolfram.com/PrimeNumberTheorem.html http://mathworld.wolfram.com/PrimeCountingFunction.html 
20031223, 00:51  #4  
Aug 2002
London, UK
5B_{16} Posts 
Quote:
I only point this out because if I don't, somebody else will (honest!). 

20031223, 15:40  #5  
∂^{2}ω=0
Sep 2002
República de California
2^{2}·3·7·139 Posts 
Quote:
I know this doesn't alter the argument, but, just for the record, it's really the Loschmidt constant, as Avogadro never made any estimate of the number itself. http://gemini.tntech.edu/~tfurtsch/scihist/avogadro.htm Last fiddled with by ewmayer on 20031223 at 15:41 

20031223, 19:44  #6 
Aug 2002
London, UK
7×13 Posts 
Touché!

20031229, 19:35  #7  
Dec 2003
Frodsham, uk
2^{2} Posts 
Quote:
Quote:
Quote:
Mathematical pedantry can be such fun. 

20031229, 19:53  #8  
Dec 2003
Frodsham, uk
2^{2} Posts 
Quote:
(The ratio of relative uncertainties in the 2 constants.) 

20031230, 15:28  #9  
∂^{2}ω=0
Sep 2002
República de California
11676_{10} Posts 
Quote:


20040127, 16:32  #10  
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}·3^{3}·19 Posts 
Who has a list?
Quote:
http://www.utm.edu/research/primes/mersenne/index.html Mally 

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