partitions.py

def sieve(n):
    is_prime = [True] * n
    primes = []
    for i in range(2, n):
        if is_prime[i]:
            primes.append(i)
            for j in range(2 * i, n, i):
                is_prime[j] = False
    return primes

n = 1000
res = [0] * n
res[0] = 1
primes = sieve(n)

for p in primes:
    for i in range(0, n):
        if i + p < n:
            res[i + p] += res[i]
            
for i in range(0, n):
    if res[i] > 5000:
        print(i)
        break