
"""simple docstring"""




from __future__ import annotations


def   __magic_name__     (				__snake_case    :	list[int | float]  )			->    int | float:
							if len(__snake_case  ) == 0:
														raise ValueError("find_min() arg is an empty sequence"  )
							lowercase   :    List[str]			=							nums[0]
							for num in nums:
														lowercase   :    List[str]			=							min(__snake_case					,			__snake_case  )
							return min_num


if __name__ == "__main__":
			import doctest

			doctest.testmod(verbose=True)




"""simple docstring"""




import math
from collections.abc import Generator


def   __magic_name__     (				__snake_case    :	int  )			->    Generator[int, None, None]:
       lowercase   :    Generator			=							(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					,			__snake_case  ):
                     if (i % j) == 0:
                            break
              else:
                     yield i


def   __magic_name__     (				__snake_case    :	int  )			->    Generator[int, None, None]:
       lowercase   :    Generator			=							(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)
              lowercase   :    Dict			=							int(math.sqrt(__snake_case  )  ) + 1
              for j in range(2					,			__snake_case  ):
                     if (i % j) == 0:
                            break
              else:
                     yield i


def   __magic_name__     (				__snake_case    :	int  )			->    Generator[int, None, None]:
       lowercase   :    Generator			=							(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):
              lowercase   :    int			=							int(math.sqrt(__snake_case  )  ) + 1
              for j in range(3					,			__snake_case					,			2  ):
                     # As we removed the even numbers, we don't need them now
                     if (i % j) == 0:
                            break
              else:
                     yield i


def   __magic_name__     (				)			->    Tuple:
       from timeit import timeit

       lowercase   :    List[str]			=							"from __main__ import slow_primes, primes, fast_primes"
       print(timeit("slow_primes(1_000_000_000_000)"					,			setup=__snake_case					,			number=100_0000  )  )
       print(timeit("primes(1_000_000_000_000)"					,			setup=__snake_case					,			number=100_0000  )  )
       print(timeit("fast_primes(1_000_000_000_000)"					,			setup=__snake_case					,			number=100_0000  )  )


if __name__ == "__main__":
   _A      :	List[Any]       		=	int(input("""Calculate primes up to:\n>> """).strip())
   for ret in primes(number):
      print(ret)
   benchmark()


