





"""simple docstring"""



from __future__ import annotations

from collections.abc import Generator







def 						__lowercase	(  )  ->Generator[int, None, None]:



    '''simple docstring'''







    __A       :		Any							=	{}
    __A       :		Dict							=	2
    while True:
        __A       :		List[Any]							=	factor_map.pop(snake_case_							,snake_case_		)
        if factor:
            __A       :		Optional[Any]							=	factor + prime
            while x in factor_map:
                x += factor
            __A       :		List[Any]							=	factor
        else:
            __A       :		Optional[int]							=	prime
            yield prime
        prime += 1







def 						__lowercase	(  snake_case_    :    int = 1e10		)  ->int:



    '''simple docstring'''







    __A       :		Optional[int]							=	sieve()

    __A       :		List[Any]							=	1
    while True:
        __A       :		Union[str, Any]							=	next(snake_case_		)
        if (2 * prime * n) > limit:
            return n
        # Ignore the next prime as the reminder will be 2.
        next(snake_case_		)
        n += 2


if __name__ == "__main__":
       print(solution())










from math import isqrt


def 					_a							(					lowerCAmelCase )->	bool:
		return all(number % divisor != 0 for divisor in range(2    ,						isqrt(lowerCAmelCase ) + 1 ) )


def 					_a							(					lowerCAmelCase = 10**6 )->	int:
		SCREAMING_SNAKE_CASE_					      =							0
		SCREAMING_SNAKE_CASE_					      =							1
		SCREAMING_SNAKE_CASE_					      =							7
		while prime_candidate < max_prime:
				primes_count += is_prime(lowerCAmelCase )

				cube_index += 1
				prime_candidate += 6 * cube_index

		return primes_count


if __name__ == "__main__":
						print(f"""{solution() = }""")