20071012, 17:23  #1 
Just call me Henry
"David"
Sep 2007
Liverpool (GMT/BST)
2^{5}×11×17 Posts 
Finding primes from 1 upwards
has anyone seached exhautively for primes particularly high
i have seached the web but cannot find any projects if not what would be the best method for starting this search 
20071012, 17:40  #2 
∂^{2}ω=0
Sep 2002
Repรบblica de California
2×11×13×41 Posts 

20071012, 17:58  #3  
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
3·11·157 Posts 
Quote:
There are some links to lists here: http://primes.utm.edu/lists/small/ 

20071012, 18:22  #4 
"Ben"
Feb 2007
3,617 Posts 
I guess it depends by what you mean by "particularly high". Here: http://www.ieeta.pt/~tos/primes.html, tables of pi(x) (the number of primes less than x) are given, and have been found/verified by the sieve of eratosthenes. It would be impractical/useless to write down all these primes. For instance, he gives pi(10^23) = 1925320391606803968923, which would take something like 17087218 peta bytes of storage if you wanted to list them all.
If you want to help find the biggest known primes, join GIMPS. Last fiddled with by bsquared on 20071012 at 18:23 
20071012, 19:08  #5 
Feb 2006
Denmark
2×5×23 Posts 
pi(x) can be computed much faster than computing all primes up to x. Only some of the pi(x) values up to pi(10^23) have been verified by the sieve of Eratosthenes. The largest exhaustive computation of primes is part of the Goldbach conjecture verification at http://www.ieeta.pt/~tos/goldbach.html. They reached 10^18 in April. pi(10^18) = 24,739,954,287,740,860 is also far too many primes to store. They were only kept shortly in ram.

20071012, 22:45  #6 
2×3^{2}×233 Posts 
Hmm, my old account (think of years, not month) is not active any more... anyways:
I still find this text about the practical limitations of computing and saving all primes to be rather good. It starts easy, but at the end it goes into detail about the limits of todays technologies. (clustering techniques etc. and where is will fail) http://www.troubleshooters.com/codec...imenumbers.htm 
20071013, 09:38  #7  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2^{2}×3×941 Posts 
Quote:
Here's a list of primes from 14 upwards: 17, 19, 23, 29, ... I'll leave you to find the primes from 1 to 14. Paul Last fiddled with by xilman on 20071013 at 09:38 Reason: Fix speeling misteaks 

20071013, 13:33  #8 
Just call me Henry
"David"
Sep 2007
Liverpool (GMT/BST)
2^{5}×11×17 Posts 
so how much disk space would it take to store the first 1,000,000 primes
i have previously written a vb.net program which uses the sieve of Eratosthenes to find all primes up to 2^30 it took about 90 second to run my program doesnt work any higher than that because the index for a bitarray has a max of (2^31)1 
20071013, 14:32  #9 
Jun 2003
7×167 Posts 

20071013, 14:41  #10  
"William"
May 2003
New Haven
2371_{10} Posts 
Quote:
http://www.rsok.com/~jrm/printprimes.html 

20071013, 16:12  #11 
Einyen
Dec 2003
Denmark
CEF_{16} Posts 
I have a file taking 285,714,288 bytes with all primes up below 10,000,000,080 using the 48 bit / 210 integers format.

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