
Re: Vindication of Goldbach's conjecture
Posted:
Jun 17, 2012 5:20 AM


On 16 juin, 20:25, Gus Gassmann <horand.gassm...@googlemail.com> wrote: > On Jun 16, 1:08 pm, mluttgens <lutt...@gmail.com> wrote: > > > > > > > On 14 juin, 16:24, Gus Gassmann <horand.gassm...@googlemail.com> > > wrote: > > > > On Jun 14, 6:28 am, mluttgens <lutt...@gmail.com> wrote: > > > > > On 10 juin, 00:20, rich...@cogsci.ed.ac.uk (Richard Tobin) wrote: > > > > > > In article <0b8c04e9f6c148c08f63c115150dd...@f30g2000vbz.googlegroups.com>, > > > > > > mluttgens <lutt...@gmail.com> wrote: > > > > > >[deleted] > > > > > > You refuse to address the question; I conclude you are a troll. > > > > > >  Richard > > > > > My response is contained in the following new version: > > > > > Vindication of Goldbach's conjecture > > > > ______________________________ > > > > > According to the conjecture, every even integer greater than 4 can be > > > > expressed as the sum of two primes. > > > > > Let's consider two identical infinite series S and S' of uneven > > > > numbers, where S and S' = 3, 5, 7, 9, 11, 13, etc... > > > > In other words, S(n) = S'(n) = 2n +1, with n beginning at 1. > > > > Let?s note that S and S? contain only natural numbers. > > > > > The fact that some uneven numbers contained in the series S and S' can > > > > be > > > > the result of mathematical operations, for instance exponentiation, is > > > > thus irrelevant. > > > > > By adding successively each number of S to all the numbers of S', one > > > > gets a series P of even numbers. > > > > > Example: > > > > _______ > > > > > n S S' > > > > _ _ _ > > > > > 1 3 3 > > > > 2 5 5 > > > > 3 7 7 > > > > 4 9 9 > > > > 5 11 11 > > > > 6 13 13 > > > > 7 15 15 > > > > 8 17 17 > > > > 9 19 19 > > > > 10 21 21 > > > > 11 23 23 > > > > > By adding, one gets the following even numbers of series P: > > > > > From S = 3: 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26 > > > > From S = 5: 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28 > > > > From S = 7: 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30 > > > > From S = 9: 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32 > > > > From S = 11: 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34 > > > > From S = 13: 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36 > > > > From S = 15: 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38 > > > > From S = 17: 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40 > > > > From S = 19: 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42 > > > > From S = 21: 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44 > > > > From S = 23: 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46 > > > > > Thus, series P contains all the even numbers from 6 to 46. > > > > > In P, the number 26 = 3+23, 5+21, 7+19, 9+17, 11+15, 13+13, 15+11, > > > > 17+9, 19+7, 21+5 and 23+3, all the terms coming from the successive > > > > uneven numbers of S and S' from 3 to 23, where 23 = 26  3. > > > > As S and S' contain all the prime numbers inferior or equal to 263 , > > > > the even number 26 is necessarily the sum of two primes. > > > > Let?s note that it is not necessary to indentify those primes. Knowing > > > > that they exist in S and S? is enough.. > > > > This applies mutatis mutandi to any even integer > > > > > Conclusion: > > > > > Every even integer greater than 4 can be expressed as the sum of two > > > > primes. > > > > In other words, the above procedure vindicates Goldbach's conjecture. > > > > It appears you do not even understand the problem. How do you *KNOW* > > > that you will never miss an even number using this schema? It is fine > > > and good to verify that every even integer less than 47 can be written > > > as a sum of two primes, but what about 83749105938571693046? Your > > > method says nothing about that number. > > > Bigger is the number, and more primes it contains. > > Hence, the number of possible sums of two primes corresponding to a > > number > > is proportional to the magnitude of the number. > > > Thus, it would be ridiculous to try a number as big as > > 83749105938571693046 > > So does the number I gave you have a representation as the sum of two > primes? And what are the two primes? (I must insist on a primality > proof.) Give me any representation. Should be easy, since you have so > many to choose from, right? >
83749105938571693046 = 157 + 83749105938571692889 = 277 + 83749105938571692769 = 283 + 83749105938571692763 = 487 + 83749105938571692559 etc... etc... etc...
Marcel Luttgens
> > > Here is an example where N is greater then 26: > > > Example: N = 138 and N3 = 135 > > ______________________________ > > > The relevant primes p are > > > 3 5 7 11 13 17 19 23 29 > > 31 37 41 43 47 53 59 61 67 71 > > 73 79 83 89 97 101 103 107 109 113 > > 127 131 > > > Np = > > > 135 133 131 127 125 121 119 115 109 > > 107 101 97 95 91 85 79 77 71 67 > > 65 59 55 49 41 37 35 31 29 25 > > 11 7 > > > Thus N = 5+133, 7+131, 11+127, 29+109, 31+107, etc... > > > Marcel Luttgens

