Prime summations

Problem 77

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?
from tools import rwh_primes2


def run(limit=5000):
    max_primeth = 101
    primes = list(rwh_primes2(max_primeth))
    primes_sum = [0] * max_primeth
    primes_sum[0] = 1
    for i in range(len(primes)):
        for j in range(primes[i], max_primeth):
            primes_sum[j] += primes_sum[j - primes[i]]

    return min(x for x in range(max_primeth) if primes_sum[x] > limit)