from tools import number_theory

def is_prime(num):
    if not num % 2:
        return False
    for p in range(3, int(num ** 0.5) + 1, 2):
        if not num % p:
            return False
    return True

def longest_slice(limit, prime):
    for l in range(len(prime)):
        if sum(prime[:l]) > limit:
            return (l - 1, sum(prime[:l - 1]))

def reduce_slice(limit, prime, start, length, tale):
    tale -= prime[start]
    start += 1
    t = tale
    while True:
        t = tale - prime[start] + prime[start + length]
        if t > limit:
            break
        tale = t
    return (start, tale)

def shift_slice(limit, prime, start, length, tale):
    for s in range(start - 1, -1, -1):
        tale = tale + prime[s] - prime[s + length]
        if is_prime(tale):
            return (tale, length)

def search(limit):
    prime = list(number_theory.make_prime(4000))
    length, tale = longest_slice(limit, prime)
    if is_prime(tale):
        return (tale, length)
    start = 0
    while length > 1:
        length -= 1
        start, tale = reduce_slice(limit, prime, start, length, tale)
        if is_prime(tale):
            return (tale, length)
        get = shift_slice(limit, prime, start, length, tale)
        if get:
            return get

print(search(1000000))