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 Goldbachs conjecture now is known as "the odd Goldbach conjecture".
"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)".
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
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:
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:
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