Prime summations

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?

Written by gamwe6 who lives and works in San Francisco building useful things. You should follow him on Twitter