



"""simple docstring"""







import math
from collections.abc import Generator


def  __SCREAMING_SNAKE_CASE (  __UpperCAmelCase      ):
		_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   ,				__UpperCAmelCase      ):
						if (i % j) == 0:
								break
				else:
						yield i


def  __SCREAMING_SNAKE_CASE (  __UpperCAmelCase      ):
		_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				: Union[str, Any]     =   int(math.sqrt(__UpperCAmelCase      )      ) + 1
				for j in range(2   ,				__UpperCAmelCase      ):
						if (i % j) == 0:
								break
				else:
						yield i


def  __SCREAMING_SNAKE_CASE (  __UpperCAmelCase      ):
		_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				: str     =   int(math.sqrt(__UpperCAmelCase      )      ) + 1
				for j in range(3   ,				__UpperCAmelCase   ,				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 (  ):
		from timeit import timeit

		_lowercase				: Tuple     =   """from __main__ import slow_primes, primes, fast_primes"""
		print(timeit("""slow_primes(1_000_000_000_000)"""   ,				setup=__UpperCAmelCase   ,				number=1000000      )      )
		print(timeit("""primes(1_000_000_000_000)"""   ,				setup=__UpperCAmelCase   ,				number=1000000      )      )
		print(timeit("""fast_primes(1_000_000_000_000)"""   ,				setup=__UpperCAmelCase   ,				number=1000000      )      )


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





'''simple docstring'''

def        SCREAMING_SNAKE_CASE_  (	snake_case_				:	int							)       ->	int:
 if number != int(snake_case_							):
  raise ValueError('factorial() only accepts integral values'							)
 if number < 0:
  raise ValueError('factorial() not defined for negative values'							)
 SCREAMING_SNAKE_CASE  :  str								=		1
 for i in range(1   ,     number + 1							):
  value *= i
 return value



def        SCREAMING_SNAKE_CASE_  (	snake_case_				:	int							)       ->	int:
 if not isinstance(snake_case_   ,     snake_case_							):
  raise ValueError('factorial() only accepts integral values'							)
 if n < 0:
  raise ValueError('factorial() not defined for negative values'							)
 return 1 if n == 0 or n == 1 else n * factorial(n - 1							)


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   __UpperCAmelCase												=   int(input('Enter a positive integer: ').strip() or 0)
   print(f"""factorial{n} is {factorial(n)}""")


