Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 Paul Posts: 780 Registered: 7/12/10
Re: conjecture on sums of primes
Posted: Feb 2, 2012 6:37 AM

On Feb 2, 10:46 am, rich...@cogsci.ed.ac.uk (Richard Tobin) wrote:
>
> 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

Date Subject Author
2/2/12 Paul
2/2/12 Richard Tobin
2/2/12 Paul
2/2/12 Richard Tobin
2/2/12 Thomas Nordhaus
2/2/12 Don Redmond
2/3/12 gnasher729
2/4/12 Butch Malahide
2/7/12 Richard Tobin
4/17/13 piman314@gmail.com
4/17/13 piman314@gmail.com
4/17/13 piman314@gmail.com
4/17/13 piman314@gmail.com
4/18/13 David Petry