Goldbach's conjecture and number of ways in which an even number can be expressed as a sum of two primes Is there a functon that counts the number of ways in which an even number can be expressed as a sum of two primes?

See Goldbach's comet at Wikipedia. 
EDIT: To expand on this a little, let $g(n)$ be the number of ways of expressing the even number $n$ as a sum of two primes. Wikipedia gives a heuristic argument for $g(n)$ to be approximately $2n/(\log n)^2$ for large $n$. Then it points out a flaw with the heuristic, and explains how Hardy and Littlewood repaired the flaw to come up with a better conjecture. The better conjecture states that, for large $n$, $g(n)$ is approximately $cn/(\log n)^2$, where $c>0$ depends on the primes dividing $n$. In all cases, $c>1.32$. 
I stress that this is all conjectural, as no one has been able to prove even that $g(n)>0$ for all even $n\ge4$. 
