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？