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Topic: Vindication of Goldbach's conjecture
Replies: 74   Last Post: Aug 9, 2012 6:50 PM

 Messages: [ Previous | Next ]
 Michael Stemper Posts: 671 Registered: 6/26/08
Re: Vindication of Goldbach's conjecture
Posted: Jun 25, 2012 12:44 PM

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.

Date Subject Author
6/6/12 mluttgens
6/6/12 Brian Q. Hutchings
6/6/12 GEIvey
6/7/12 Richard Tobin
6/8/12 mluttgens
6/8/12 Count Dracula
6/9/12 mluttgens
6/9/12 Brian Q. Hutchings
6/9/12 mluttgens
6/25/12 GEIvey
6/9/12 Richard Tobin
6/9/12 mluttgens
6/9/12 Richard Tobin
6/9/12 Brian Q. Hutchings
6/9/12 Brian Q. Hutchings
6/14/12 mluttgens
6/16/12 mluttgens
6/16/12 Frederick Williams
6/20/12 mluttgens
6/20/12 Rick Decker
6/21/12 mluttgens
6/21/12 Frederick Williams
6/21/12 mluttgens
6/22/12 mluttgens
6/22/12 mluttgens
6/22/12 Brian Q. Hutchings
6/25/12 Michael Stemper
6/26/12 mluttgens
6/26/12 Frederick Williams
6/28/12 Michael Stemper
7/19/12 mluttgens
7/19/12 Timothy Murphy
7/19/12 mluttgens
7/19/12 Gus Gassmann
7/20/12 mluttgens
8/1/12 Tim Little
8/4/12 mluttgens
8/4/12 Frederick Williams
8/6/12 mluttgens
8/6/12 gus gassmann
8/6/12 Brian Q. Hutchings
8/9/12 Pubkeybreaker
7/19/12 J. Antonio Perez M.
7/20/12 mluttgens
6/25/12 Michael Stemper
6/25/12 Thomas Nordhaus
6/17/12 mluttgens
6/17/12 quasi
6/18/12 Count Dracula
6/18/12 quasi
6/19/12 Count Dracula
6/19/12 quasi
6/20/12 mluttgens
6/22/12 Michael Stemper
6/22/12 mluttgens
6/22/12 Robin Chapman
6/22/12 Michael Stemper
6/23/12 mluttgens
6/22/12 Richard Tobin
6/22/12 Richard Tobin
6/25/12 Richard Tobin
6/25/12 Michael Stemper
6/14/12 Count Dracula
6/21/12 Luis A. Rodriguez
6/21/12 Brian Q. Hutchings
6/21/12 mluttgens
6/25/12 GEIvey
6/20/12 J. Antonio Perez M.