Am 02.02.2012 12:53, schrieb Richard Tobin: > In article<email@example.com>, > Paul<firstname.lastname@example.org> wrote: >> Does anyone know of any large near counter-examples to Goldbach's >> conjecture? > > I have not heard that there are any. > >> For example, what's the largest known even number that >> can be expressed as the sum of two primes in only 1 way? > > As far as I know, 12.
Cf. OEIS A000954 for example. I made a little survey, looking for the "largest relative drop in the number of Goldbach-partitions r(2n) between consecutive even numbers". Maybe that counts as "near-counterexample".
In the range 4 <= 2n <= 10000 I found r(630)=41, r(632)=10. Actually n=632 is conjectured to be the largest n with exactly 10 partitions, see A000954.