
Re: conjecture on sums of primes
Posted:
Feb 2, 2012 9:56 AM


Am 02.02.2012 12:53, schrieb Richard Tobin: > In article<8faccb56a9664767b7c2206e11a6e7da@o14g2000vbo.googlegroups.com>, > Paul<pepstein5@gmail.com> wrote: >> Does anyone know of any large near counterexamples 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 Goldbachpartitions r(2n) between consecutive even numbers". Maybe that counts as "nearcounterexample".
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.
 Thomas Nordhaus

