In article <firstname.lastname@example.org>, mluttgens <email@example.com> writes: >On 21 juin, 15:08, Frederick Williams <freddywilli...@btinternet.com> wrote: >> mluttgens wrote:
>> > It was easy to show that the even number 26 is the sum of two primes: >> >> > 26 =3D 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. =A0You've gone up to 100,000 (have you eve= >n >> 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
Funny, for 60119912, I get 288046 pairs.
-- Michael F. Stemper #include <Standard_Disclaimer> Life's too important to take seriously.