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Re: Vindication of Goldbach's conjecture
Posted:
Jun 25, 2012 12:44 PM
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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.
--
Michael F. Stemper
#include <Standard_Disclaimer>
Life's too important to take seriously.
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