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September 22nd, 2011, 05:28 PM  #1 
Newbie Joined: Sep 2011 Posts: 1 Thanks: 0  Proof of Goldbach's conjecture
and twin prime, GreenTao, MarieSophie Germain, Riemann, and so on. when apply a little, ax^2+bx+c 
September 22nd, 2011, 06:10 PM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Proof of Goldbach's conjecture
Line 1. Is it or or something else? I assume is the kth prime, though this is not standard notation. Line 1. What are maximal terms, what do they depend on, and does the result here apply to any maximal term or just some maximal term? Line 2. Again, what is the product over? You should really put multiplication and addition that does not apply to each term separately on the left and use parentheses if you have multiple terms on the right. Line 3. You say this is a density, but do you mean a prime count? If not, what sort of density do you mean  multiplicative, logarithmic, natural, Schnirelmann, Dirichlet, something else? (I skipped some lines here; I believe the result in this intermediate section because of Mertens' theorem so I needn't check your version.) Line 12. This is false for every i and numbers sufficiently large. For example, it is false for numbers larger than 33 for i = 2. (Check this for 34: 11/34 < 1/3. I'll leave it as an exercise to show that this holds for all larger numbers, tiresome but not difficult.) At first I thought perhaps you meant something other than "prime" in line 12, but you use the result in subsequent lines as though it was prime. It looks like line 12 is the first fatal flaw in the proof. 

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