mluttgens wrote: > > 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?
> > 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: > > N n > _ _ > > 50 8 > 100 12 > 500 26 > 1000 56 > 5000 152 > 10000 254 > 50000 900 > 100000 1628 > > Clearly, when N increases, the number of Goldbach's sums also > increases.
There's no 'clearly' about it. You've gone up to 100,000 (have you even done that, or just looked at some numbers up to 100,000?); what about N > 100,000?
-- The animated figures stand Adorning every public street And seem to breathe in stone, or Move their marble feet.