(Edited according to the comments below)
In 'Old and New Problems and Results in Combinatorial Number Theoryhis article titled 'Sums of Erdos and GrahamDistinct Primes', it is said that Kløve conjecturedin 'Sums of Distinct Elements from a Fixed Set' (which can be found on jstor, although I haven't read it)on the basis of computational evidence, that $\lim_{x \displaystyle \lim_{x \rightarrow \infty} \dfrac{N_x}{x} = 3$, which implies Goldbach.
EDIT: Apparently This would imply the reference of Erdos and Graham is incorrect binary Goldbach conjecture (see for large enough $x$) in the comments below), so maybe they meant to refer to a different article from Kløve, titledfollowing way: 'Sums if every integer larger than $(3 + \epsilon)x$ can be written as sum of Distinct Primes'. All the evidence I have for this suggestion is the title itself. Anywayprimes, I very much doubt they where those primes are wrong about the conjectureall larger than $x$, then, which seems reasonablein particular, every even number between $(3 + \epsilon)x$ and $4x$ can be written as a sum of two primes.
