Goldbach Partitions

Intuitive reasoning has led me to develop a simple approximation, which contains factors different from those used in well knoen formulas. Numerically, "my" formula delivers results, which are almost as accurate, as Hardy-Littlewood`s with the Shah-Wilson correction.

Attached Files
 Goldbach.pdf (217.6 KB, 40 views)
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 Recognitions: Homework Help Science Advisor The formula (2) has a typo or is otherwise ill-posed. I trust from the parenthetical comment that the intent is $$\frac12\pi(n)\prod_{3  Thank you indeed, CRGreathouse, for signalling this error. Using Merten's Theorem, I find, that g_alt must be divided by 2*exp(-gamma)=1,122918967..., with gamma=0,577215664901... being Euler-Mascheroni's constant. Then, g_alt will be asymptotically equivalent to g_HL I'm now working on correcting the derivation of (2) Best Regards - Marchal Goldbach Partitions Here is a revised version of my article. Attached Files  Goldbach2.pdf (657.5 KB, 6 views)  Recognitions: Homework Help Science Advisor I wrote several paragraphs of response but the forum ate it, grr. In short: There are about two dozen errors in the first few pages, but they're mostly minor and correctable. By page 3 you use notations that are not only nonstandard but for which I can't even find any valid interpretation. Unfortunately your use of ≈ rather than, say, ~ makes your statements non-testable (and even non-falsifiable in a Poperian sense).  Dear CBGreathouse Thanks for reviewing my text with so much attention!. In standard notation I should write n[tex]\neq$$0 (modp) (equation 2a) q$$\neq$$0 (modp) and q$$\neq$$n (modp) (equation 2.2.1) I changed the equivalence symbols, as you suggested (see attachment).

Attached Files
 Goldbach3.pdf (661.2 KB, 7 views)
 Recognitions: Homework Help Science Advisor 1.2 still has issues. It's C_2 not C_HL and the "<= infinity" should be dropped. (There are rare cases where you want to write "< infinity" for clarity, but this isn't one and certainly "<= infinity" is just wrong.) 2a confuses me; what's the definition of g_alt? If this is supposed to be the definition you need = not ~ (or one of the defined-as symbols, if you prefer). For congruences you need ≡ ≢ not = ≠ . Have to go now; might look at p. 3 ff. later.

I still worked on page 3. Here it comes with corrections.
Attached Files
 page 3.pdf (273.9 KB, 1 views)

Please ignore my last message. Here comes page3-improved version.
Attached Files
 page 3 improved version.pdf (282.1 KB, 8 views)
 Recognitions: Homework Help Science Advisor 2.2.2 is the first questionable part: you claim that one obtains asymptotic equivalence. (You mark it an estimate, but then write ~.) This heuristic has been well-known for hundreds of years, but a proof is lacking. This is what you'd expect if the primes fell 'randomly', but it's not clear that they do in an appropriate fashion.
 Thanks, Greg. I fully agree. Besides, I suspect my deduction to be substantially erronous. I'll need some time to clarify the matter. Until then Marchal

Here I am again! For correct formula & deduction, see APPENDIX attached.
Attached Files
 APPENDIX.pdf (396.8 KB, 2 views)