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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?