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 1 - distributed.net
  A distributed computing project currently trying to take the RSA challenge of RC5-64, and also working on OGR-24 and 25 (Optimal Golomb Rulers). Previous projects included CSC and DES.
http://www.distributed.net/
 
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 2 - The Prime Pages
  Prof. Chris Caldwell's database of virtually every large or otherwise interesting prime number known; includes the 5,000 largest known prime numbers and records for specific types.
http://primes.utm.edu/
 
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 3 - Great Internet Mersenne Prime Search
  Online search for Mersenne prime numbers, found largest several primes.
http://www.mersenne.org/
 
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 4 - RSA Security - Challenges
  Monetary prizes for factoring certain large numbers ("RSA Numbers"), as well as breaking RSA and DES encryption schemes; announcements mailing list.
http://www.rsasecurity.com/rsalabs/node.asp?id=2091
 
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 5 - ECMNET
  Project to factor numbers using the elliptic curve method. Client and server software.
http://www.loria.fr/~zimmerma/records/ecmnet.html
 
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 6 - Electronic Frontier Foundation
  Cash prizes for discovery of very large prime numbers through Cooperative Computing Awards program.
http://www.eff.org/awards/coop.html
 
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 7 - Seventeen Or Bust
  A distributed attack on the Sierpinski problem, trying to find the last remaining 17 numbers.
http://www.seventeenorbust.com
 
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 8 - Ellipsa - Elliptic Curve Primality Proving
  Primo, a primality proving program based on the ECPP algorithm. With Primo one can check crypto-primes and prove whether or not they are actually prime.
http://www.ellipsa.net/
 
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 9 - MM61
  Attempt at factoring the huge Mersenne number 2^(2^61-1)-1. Software for Windows, DOS and Linux. Work reservation via email.
http://www.ltkz.demon.co.uk/ar2/mm61.htm
 
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 10 - Generalized Fermat Primes Search
  Project provides software to search for primes of a specific form. Coordinated via email.
http://perso.wanadoo.fr/yves.gallot/primes/index.html
 
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