On 21 juin, 19:50, luir...@yahoo.com wrote: > El jueves, 14 de junio de 2012 10:24:12 UTC-4:30, Count Dracula escribió: > > > > > > > On Jun 14, 5:28 am, mluttgens <lutt...@gmail.com> wrote: > > > 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 26-3 , > > > 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.. > > > The argument you give here is fallacious. The sets S and S' also > > contain odd > > numbers that are not prime. This makes it necessary to identify the > > particular > > primes and it is not enough to know that primes exist in S and S'. In > > your > > example for 26, it is not possible to use the sums 5+21, 9+17, 11+15, > > 15+11, > > 17+9, 21+5 since each contains a composite integer. My earlier > > question to you was: what if there is an integer for which _all_ the > > sums > > are inadmissable, not just some as in the case of 26? Nothing in your > > argument rules out this possibility. > > > If a counterexample exists it will have to be larger that 10^17 > > because > > computer verifications have been performed up to about that value. A > > correct > > proof is highly likely to require some highly technical innovations. > > > Count Dracula > > The true difficult with Goldbach's Conjecture is this: > Given a even number 2k to warrant that the pairing of the > two arithmetic progressions 2n + 1 and 2k - (2n+1) will produce > nor less than one coincidence of two primes. > Example.- Given the even number 98. The two progressions are: > > 3, 5, 7, 9, 11, 13, 15, 17,.........95 > 95, 93, 91, 89, 87, 85, 83, 81,......... 3 > > Who guarantee that there will be a column with two primes? > > Ludovicus > >
All you need is a little software, which will give you all the Goldbach's pairs.