not yet a conventional proof of Goldbach #5.29 Correcting Math
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From: Archimedes Plutonium on 13 Aug 2010 01:59 It may not be obvious to some viewers that I have not yet achieved a proof of Goldbach. Sometimes in excitement I overstate things. Goldbach is not yet here, proven. It would be proven if I had a Galois Algebra that could mirror image multiplication with addition since in multiplication, every Even Integer >2 requires a decomposition into at minimum two prime factors. So if multiplication were interchangeable with addition, Goldbach would instantly be proven true. It reminds me of the proofs in Projective Geometry where theorems on lines are interchangeable with the same theorems by translation into points. So can we substitute lines for multiplication and points for addition and do a Projective Geometry proof of Goldbach? Perhaps mathematics in the 22nd century will be trespassing into this new arena of mathematics. But here I am trying to make a conventional proof out of Goldbach, if that is possible, or like Fermat's Last Theorem or the Riemann Hypothesis, perhaps, Goldbach is amongst those that can only be proven up to 10^500 and hence true. And that no conventional proof is able because Goldbach has counterexamples in the AP-adics Infinite Integers. The good news so far, is that I truly do have proofs of Infinitude of Twin Primes, Polignac, Mersenne Primes, Infinitude of Perfect Numbers and a proof that No Odd Perfect Numbers, other than 1 Exist. It is just that Goldbach is hung up. What I need to make the above a conventional proof is a theorem that says something along these lines of the Goldbach Repair Kit. Let us say I am given an Even Integer like 100 and let me suppose that Goldbach breaks down at 100, then 98 is the last time that Goldbach was still good and that 98 has (61,37) as Goldbach summands. What I need as a theorem to prove Goldbach is that by a recursive manipulation of 61 and 37 (61,37) with adding 2 to find two new prime summand pair (61,37) with adding 4 but subtracting 2 to find two new prime summand pair (61,37) with adding 6 but subtracting 4 to find two new prime summand pair ad infinitum If there is a theorem that can be proven that given any Goldbach summand pair for Even Integers >6 that the process above always insures a new two prime summand pair. So I have reduced the Goldbach Conjecture to a theorem that says basically every Even Integer >6 has a new prime summand pair out of the Repair Kit (K-2,2) Now in the 1990s I was using the Chebychev theorem that between M and 2M always exists a prime, but I do not think Chebychev theorem is applicable here. The above has more of a hint to Polignac of primes spaced apart by a 2k metric. Archimedes Plutonium http://www.iw.net/~a_plutonium/ whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies |