On 21 juin, 15:08, Frederick Williams <freddywilli...@btinternet.com> wrote: > 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?
For N = 1000000, one gets 10804 Goldbach's pairs. The relation between log N and log n is log n = 0.727*log N -0.436 For N = 60,119,912, log n = 5.219 and the number of pairs is 165577
> > -- > The animated figures stand > Adorning every public street > And seem to breathe in stone, or > Move their marble feet.