Paul
Posts:
516
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: > In article <04113ffdb6f84092a93955aff8c18...@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 counterexamples 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

