  Let $\Sigma_{2n}$ be the set of all partitions of the even integers from the
interval $(4,2n], n>2,$ into two odd prime parts. We show that
$\mid\Sigma_{2n}\mid\sim 2n^2/\log^2{n}$ as $n\to\infty$. We also assume that a
partition is selected uniformly at random from the set $\Sigma_{2n}$. Let
$2X_n\in (4,2n]$ be the size of this partition. We prove a limit theorem which
establishes that $X_n/n$ converges weakly to the maximum of two random
variables which are independent copies of a uniformly distributed random
variable in the interval $(0,1)$. Our method of proof is based on a classical
Tauberian theorem due to Hardy, Littlewood and Karamata. We also show that the
same asymptotic approach can be applied to partitions of integers into an
arbitrary and fixed number of odd prime parts
