





"""simple docstring"""





import math
from collections.abc import Generator


def    a__       (       _SCREAMING_SNAKE_CASE     ):




		"""simple docstring"""


		UpperCamelCase =						(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	,						_SCREAMING_SNAKE_CASE     ):
						if (i % j) == 0:
								break
				else:
						yield i


def    a__       (       _SCREAMING_SNAKE_CASE     ):




		"""simple docstring"""


		UpperCamelCase =						(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)
				UpperCamelCase =						int(math.sqrt(_SCREAMING_SNAKE_CASE     )     ) + 1
				for j in range(2	,						_SCREAMING_SNAKE_CASE     ):
						if (i % j) == 0:
								break
				else:
						yield i


def    a__       (       _SCREAMING_SNAKE_CASE     ):




		"""simple docstring"""


		UpperCamelCase =						(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):
				UpperCamelCase =						int(math.sqrt(_SCREAMING_SNAKE_CASE     )     ) + 1
				for j in range(3	,						_SCREAMING_SNAKE_CASE	,						2     ):
						# As we removed the even numbers, we don't need them now
						if (i % j) == 0:
								break
				else:
						yield i


def    a__       (       ):




		"""simple docstring"""


		from timeit import timeit

		UpperCamelCase =						"from __main__ import slow_primes, primes, fast_primes"
		print(timeit("slow_primes(1_000_000_000_000)"	,						setup=_SCREAMING_SNAKE_CASE	,						number=1_000_000     )     )
		print(timeit("primes(1_000_000_000_000)"	,						setup=_SCREAMING_SNAKE_CASE	,						number=1_000_000     )     )
		print(timeit("fast_primes(1_000_000_000_000)"	,						setup=_SCREAMING_SNAKE_CASE	,						number=1_000_000     )     )


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













"""simple docstring"""





from ..utils import DummyObject, requires_backends





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Union[str, Any]:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Any:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Dict:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Optional[Any]:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Tuple:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Union[str, Any]:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Optional[int]:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Optional[Any]:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Union[str, Any]:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> int:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> List[Any]:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Tuple:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Dict:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Any:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Optional[Any]:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Dict:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Any:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Dict:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> List[str]:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Tuple:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Tuple:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> int:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Optional[Any]:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> int:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Tuple:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Tuple:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> str:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Optional[int]:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Optional[Any]:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Union[str, Any]:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> int:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Any:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Dict:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Optional[int]:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Optional[int]:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Union[str, Any]:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> int:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> List[Any]:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Dict:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Dict:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> List[Any]:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Optional[int]:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Tuple:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> List[Any]:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> List[str]:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> str:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> int:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Dict:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> List[Any]:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> List[str]:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> int:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Optional[int]:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> int:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> str:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> str:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> int:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Dict:
								requires_backends(self ,				["tokenizers"]		)





class 							_lowerCamelCase   (							metaclass=_lowercase			):
						UpperCAmelCase_			=      ["tokenizers"]


						def __init__(self ,				*__a ,				**__a		)			-> Dict:
								requires_backends(self ,				["tokenizers"]		)






