It is possible to write ten as the sum of primes in exactly five different ways:
$$\begin{align} &7 + 3\\ &5 + 5\\ &5 + 3 + 2\\ &3 + 3 + 2 + 2\\ &2 + 2 + 2 + 2 + 2 \end{align}$$What is the first value which can be written as the sum of primes in over five thousand different ways?
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