Problems & Puzzles: Conjectures

Conjecture 1. Goldbach's Conjecture 

"In a letter of 1742 to Euler, Goldbach expressed the belief that ‘Every integer N>5 is the sum of three primes’. Euler replied that this is easily seen to be equivalent to the following statement : ‘Every even integer 2n=>4 is the sum of two primes’ (Ref. 1, p. 291) 

Then as we can see the original idea was from Goldbach but the simplification and limitation of it came from Euler. 

By the above reasons the original statement of the Goldbach’s conjecture now is known as "the odd Goldbach conjecture". 

*** 
Samuli Larvala send today (11/08/98) the following interesting information about the status of the work done over this conejcture: 

"Matti Sinisalo has checked the conjecture up to 4*10^11. His paper was published in Math.Comp. "M.K. Sinisalo, Checking the Goldbach conjecture up to 4*10^11, Math. Comp. 61 (1993)". 

J-M. Deshouillers and Herman te Riele have recently checked it up to 10^14. They published a preview paper on their work when they had reached 10^13. This paper can be found at:
ftp://ftp.cwi.nl/pub/herman/Goldbach/gold13.ps  

On te Riele's web page they say they've now checked it up to 10^14 and the paper will be published soon. The web-page can be found at:
http://dbs.cwi.nl/cwwwi/owa/cwwwi.print_projects?ID=12 (currently broken, 1/9/01) 

Joerg Richstein from the Institute of Informatics, Justus-Liebig-University, announces his results (July 27th, 1998) about "Verifying Goldbach's Conjecture up to 4 x 1014" at:
http://www.informatik.uni-giessen.de/staff/richstein/ca/Goldbach.html 

M.L. Perez comments (6/7/99) that "The Goldbach Conjecture has been generalized in the form of the  SMARANDACHE CONJECTURE" that can be seen at: http://www.gallup.unm.edu/~smarandache/prim-sum.txt


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