On 16 juin, 19:00, Frederick Williams <freddywilli...@btinternet.com> wrote: > mluttgens wrote: > > > 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. > > That's a big claim. Can you prove it? > > -- > The animated figures stand > Adorning every public street > And seem to breathe in stone, or > Move their marble feet. > >
It was easy to show that the even number 26 is the sum of two primes:
26 = 3+23, 7+19, 13+13, 19+7 and 23+3.
Let's call those sums Goldbach's sums. The number 26 has thus 5 Goldbach's sums. Hence, the number 26 vindicates Goldbach's conjecture.
In order to falsify the conjecture, one should need to show that some even number can't be the sum of two primes.
Hereafter are the numbers n of Goldbach's sums for increasing even numbers N:
Clearly, when N increases, the number of Goldbach's sums also increases. Perhaps could somebody finds a formula linking N and n. The given example shows that n cannot decrease from some value of N and eventually becomes zero. Thus, it vindicates Goldbach's conjecture.