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Topic: conjecture on sums of primes
Replies: 13   Last Post: Apr 18, 2013 12:45 AM

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Paul

Posts: 387
Registered: 7/12/10
Re: conjecture on sums of primes
Posted: Feb 2, 2012 6:37 AM
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On Feb 2, 10:46 am, rich...@cogsci.ed.ac.uk (Richard Tobin) wrote:
> In article <04113ffd-b6f8-4092-a939-55aff8c18...@z31g2000vbt.googlegroups.com>,
>
> Paul  <pepste...@gmail.com> wrote:

> >I conjecture that, for all integers N > 1, there exists an integer E
> >such that E can be expressed as the sum of two primes in more than N
> >different ways.

>
> To convince yourself (rather than prove) that this is true, consider
>
>  http://www.cogsci.ed.ac.uk/~richard/goldbach.html
>
> Since creating that graph, I have learnt that it is known as Goldbach's
> Comet.



Your graph is interesting, but it may be possible to show that
Goldbach's Comet can mislead the intuition.
For example, if there is a very large x (say > 10^18) which can be
expressed as the sum of two primes in very few ways (for example < 10
ways), then the limitations of such graphs would be shown.

Does anyone know of any large near counter-examples to Goldbach's
conjecture? For example, what's the largest known even number that
can be expressed as the sum of two primes in only 1 way?

Does anyone know any results/tables for the largest known even number
E_k that can be expressed as the sum of two primes in <= k ways?

Paul Epstein




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