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

~~~
7 + 3
5 + 5
5 + 3 + 2
3 + 3 + 2 + 2
2 + 2 + 2 + 2 + 2
~~~

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