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

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Thomas Nordhaus

Posts: 433
Registered: 12/13/04
Re: conjecture on sums of primes
Posted: Feb 2, 2012 9:56 AM
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Am 02.02.2012 12:53, schrieb Richard Tobin:
> In article<8faccb56-a966-4767-b7c2-206e11a6e7da@o14g2000vbo.googlegroups.com>,
> Paul<pepstein5@gmail.com> 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.

--
Thomas Nordhaus



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