"""
The prime 41, can be written as the sum of six consecutive primes:
    41 = 2 + 3 + 5 + 7 + 11 + 13
This is the longest sum of consecutive primes that adds to a prime below one-hundred.

The longest sum of consecutive primes below one-thousand that adds to a prime, contains 21 terms,
and is equal to 953.

Which prime, below one-million, can be written as the sum of the most consecutive primes?
"""

import time


def timer(func):
    def wrapper(*args, **kwargs):
        start_time = time.time()
        result = func(*args, **kwargs)
        end_time = time.time()
        elapsed_time = end_time - start_time
        print(f"{func.__name__} time: {elapsed_time:.6f} seconds")
        return result

    return wrapper


def primes_list(limit: int = 10**6) -> list[int]:
    if limit < 2:
        return []

    is_prime = bytearray(b"\x01") * limit
    is_prime[0:2] = b"\x00\x00"  # 更简洁的写法，同时置0和1

    # 埃氏筛，使用切片赋值加速
    # int(limit**0.5) 等价于 isqrt(limit)（Python 3.8+ 可用 math.isqrt）
    for i in range(2, int(limit**0.5) + 1):
        if is_prime[i]:
            start = i * i
            # 计算切片长度：从 start 到 limit，步长 i 的元素个数
            count = (limit - start + i - 1) // i  # 等效于 ceil((limit-start)/i)
            if count > 0:
                is_prime[start:limit:i] = b"\x00" * count

    return [i for i in range(limit) if is_prime[i]]


def max_primes_sum(limit: int = 10**6) -> tuple:
    primes = primes_list(limit)
    prime_set = set(primes)

    # 计算从2开始连续加素数，最多能加多少个不超过limit
    max_possible_len = 0
    temp_sum = 0
    for p in primes:
        temp_sum += p
        if temp_sum >= limit:
            break
        max_possible_len += 1

    # 从最长可能长度往下枚举
    for length in range(max_possible_len, 0, -1):
        # 滑动窗口：计算连续length个素数的和
        window_sum = sum(primes[:length])
        if window_sum >= limit:
            continue

        # 滑动窗口遍历所有起始位置
        for start in range(len(primes) - length):
            if window_sum in prime_set:
                return window_sum, length
            # 滑动：减去头部，加上尾部
            window_sum += primes[start + length] - primes[start]
            if window_sum >= limit:
                break

    return 0, 0


@timer
def main():
    limit = int(input("limit:"))
    max_sum, max_length = max_primes_sum(limit)
    print(f"max primt: {max_sum}, max_length: {max_length}")


if __name__ == "__main__":
    main()