  We discuss $Q(n)$, the number of ways a given integer $n$ may be written as a
sum of distinct primes, and study its asymptotic form $Q_{as}(n)$ valid in the
limit $n\to\infty$. We obtain $Q_{as}(n)$ by Laplace inverting the fermionic
partition function of primes, in number theory called the generating function
of the distinct prime partitions, in the saddle-point approximation. We find
that our result of $Q_{as}(n)$, which includes two higher-order corrections to
the leading term in its exponent and a pre-exponential correction factor,
approximates the exact $Q(n)$ far better than its simple leading-order
exponential form given so far in the literature.
