improving my Goldbach proof without needing Galois Algebra #5.20 Correcting Math
in [Logic]
|
Prev: UK maths deterioration; UK math poster believes K is not divisible by K nor by 1; UK math insanity
Next: improving my Goldbach proof without needing Galois Algebra #5.21 Correcting Math
From: Archimedes Plutonium on 12 Aug 2010 00:30 Archimedes Plutonium wrote: > Archimedes Plutonium wrote: > (others snipped) > > > > Proof of Goldbach: Every even number >2 is the sum of at least two > > primes. Every > > even number >2 is the product of at least 2 primes, for example 4 is > > 2x2, 8 is 2x2x2, > > 6 is 2x3. Notice the symmetry, that all even numbers are at least the > > product of two > > primes translates into all even numbers >2 must be at least the sum of > > two primes. > > Now 8 is both 2+2+2+2 but also 3+5. So is that a detriment to the > > proof? Not at all. > > Because the key idea is that there is no even number >2 that is the > > product of only one > > single prime. So we see here, how Algebra of multiplication translates > > into addition. > > > > Now what is especially intriguing about the proof of Goldbach is that > we see an locking > together of Galois Algebra of addition and multiplication in one proof > that has never > before been seen in the history of mathematics. It has immense > implications for other proofs > such as Riemann Hypothesis for there we have another example of a > series of addition equal to a (series) of multiplication. > > So that in the proof of Goldbach, it is true because every even > Natural >2 has at minimum two > prime number factors and so every even Natural >2 must have at least > two prime numbers as > sums. If there exists one Natural >2 that is the sum of a singlet > prime with a composite and no two primes yields the sum, then there > exists a Even Natural >2 whose prime decomposition has only a singlet > prime factor. > > So what is the Galois Algebra that says addition is interchangeable > with multiplication? > The more I think about this, the more I realize I do not need the Algebra of interchange between multiplication and addition, where both require a minimum of two primes for every Even Number >2. Let me crudely write out the proof, continually improving it. PROOF: (1) Every Even Natural >2 has at minimum two prime factors in a decomposition. For example 6 = 2 x 3 (2) Hypothetically assume there is a Even Natural >2, call it K, that has no two prime summands which added together equals K. (3) Now K has at least two prime factors in a decomposition of multiplication (4) Now let me use an example to guide this proof of that of 12 which to Goldbach would be 7 + 5. But as an example, say it only had one prime such as 10 + 2. (5) Now can I achieve a contradiction (6) I think I can, and maybe I do not even need the multiplication lemma that every even number >2 has two prime divisors. (7) Without loss to argument take 2 as the singlet prime in Goldbach then we have the Goldbach pairs as (K-2, 2), such as the (10,2) for 12. (8) But then 10 or K-2 has two prime summands. And in this case they are (5,5) (9) This is almost looking like a Ferrmat's Infinite Descent or Mathematical Induction. (10) So we have the decomposition of K into (K-2, 2) and the decomposition of K-2 into (p_1, p_2) (11) Now, all I need is the idea that if I add 2 to that of either p_1 or p_2, I end up with two prime summands. (12) looking good and shaping up good and nicely, because it looks like a mathematical induction for a Goldbach proof, where the idea is that if Goldbach breaks down somewhere it is a even number called K and we can then utilize K-2, and 2 as summands and that we know K-2 obeys Goldbach, that all I have to retrieve is the adding of 2 to either the p_1 or p_2 yields two prime summands. Maybe, or maybe not, the multiplication lemma comes in handy. tired now and will continue later.... 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 |