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Re: Vindication of Goldbach's conjecture
Posted:
Jun 25, 2012 1:33 PM
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Am 25.06.2012 18:44, schrieb Michael Stemper:
> In article <bcdd45cd-c041-4248-a849-c905ec280557@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
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