






import math
from collections.abc import Generator



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





    """simple docstring"""

    __A             =		(i for i in range(1     ,			(max_n + 1)      ))
    for i in (n for n in numbers if n > 1):
        for j in range(2     ,			__lowercase      ):
            if (i % j) == 0:
                break
        else:
            yield i



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





    """simple docstring"""

    __A             =		(i for i in range(1     ,			(max_n + 1)      ))
    for i in (n for n in numbers if n > 1):
        # only need to check for factors up to sqrt(i)
        __A             =		int(math.sqrt(__lowercase      )      ) + 1
        for j in range(2     ,			__lowercase      ):
            if (i % j) == 0:
                break
        else:
            yield i



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





    """simple docstring"""

    __A             =		(i for i in range(1     ,			(max_n + 1)     ,			2      ))
    # It's useless to test even numbers as they will not be prime
    if max_n > 2:
        yield 2  # Because 2 will not be tested, it's necessary to yield it now
    for i in (n for n in numbers if n > 1):
        __A             =		int(math.sqrt(__lowercase      )      ) + 1
        for j in range(3     ,			__lowercase     ,			2      ):
            # As we removed the even numbers, we don't need them now
            if (i % j) == 0:
                break
        else:
            yield i



def      _SCREAMING_SNAKE_CASE  (	)  -> Union[str, Any]:





    """simple docstring"""

    from timeit import timeit

    __A             =		"""from __main__ import slow_primes, primes, fast_primes"""
    print(timeit("""slow_primes(1_000_000_000_000)"""     ,			setup=__lowercase     ,			number=1_0_0_0_0_0_0      )      )
    print(timeit("""primes(1_000_000_000_000)"""     ,			setup=__lowercase     ,			number=1_0_0_0_0_0_0      )      )
    print(timeit("""fast_primes(1_000_000_000_000)"""     ,			setup=__lowercase     ,			number=1_0_0_0_0_0_0      )      )


if __name__ == "__main__":
  __a :    Dict								=				int(input("Calculate primes up to:\n>> ").strip())
  for ret in primes(number):
    print(ret)
  benchmark()












from ..utils import DummyObject, requires_backends


__a :    int								=				None



def      _SCREAMING_SNAKE_CASE  (	*__lowercase				:     Any     ,			**__lowercase				:     Optional[int]      )  -> Tuple:





    """simple docstring"""

    requires_backends(__lowercase     ,			["""sentencepiece""", """tokenizers"""]      )




