
Re: Vindication of Goldbach's conjecture
Posted:
Jun 25, 2012 1:33 PM


Am 25.06.2012 18:44, schrieb Michael Stemper: > In article <bcdd45cdc0414248a849c905ec280557@fr28g2000vbb.googlegroups.com>, mluttgens <luttgma@gmail.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.
Affirmative. I get 144023 ordered pairs.
 Thomas Nordhaus

