





import math
from collections.abc import Generator





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





def   _lowercase       (    _UpperCAmelCase					)    ->	Generator[int, None, None]:
				lowerCamelCase									=(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):
								lowerCamelCase									=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   _lowercase       (    )    ->	Dict:
				from timeit import timeit

				lowerCamelCase									="""from __main__ import slow_primes, primes, fast_primes"""
				print(timeit("""slow_primes(1_000_000_000_000)"""      ,   setup=_UpperCAmelCase      ,   number=1_00_00_00					)					)
				print(timeit("""primes(1_000_000_000_000)"""      ,   setup=_UpperCAmelCase      ,   number=1_00_00_00					)					)
				print(timeit("""fast_primes(1_000_000_000_000)"""      ,   setup=_UpperCAmelCase      ,   number=1_00_00_00					)					)


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












def   _lowercase       (    _UpperCAmelCase					)    ->	bool:
				if not isinstance(_UpperCAmelCase      ,   _UpperCAmelCase					):
								lowerCamelCase									=F"""Input value of [number={number}] must be an integer"""
								raise TypeError(_UpperCAmelCase					)
				if number < 0 or number % 2 == 1:
								return False
				lowerCamelCase									=int(number**0.5					)
				return number == number_sqrt * (number_sqrt + 1)


if __name__ == "__main__":
							import doctest

							doctest.testmod()





