Problem 77

Prime summations

It is possible to write ten as the sum of primes in exactly five different ways:

$$
\begin{aligned}
&7 + 3\\
&5 + 5\\
&5 + 3 + 2\\
&3 + 3 + 2 + 2\\
&2 + 2 + 2 + 2 + 2
\end{aligned}
$$

What is the first value which can be written as the sum of primes in over five thousand different ways?

将$10$写成素数的和，有$5$种不同的方式：

$$
\begin{aligned}
&7 + 3\\
&5 + 5\\
&5 + 3 + 2\\
&3 + 3 + 2 + 2\\
&2 + 2 + 2 + 2 + 2
\end{aligned}
$$

最小的能以超过$5000$种不同的方式写成素数之和的数是多少？