"""simple docstring"""




import math
from collections.abc import Generator



def 				__a       (			_lowercase						):







					"""simple docstring"""





					lowerCamelCase__		:   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							, _lowercase						):
															if (i % j) == 0:
																				break
										else:
															yield i



def 				__a       (			_lowercase						):







					"""simple docstring"""





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



def 				__a       (			_lowercase						):







					"""simple docstring"""





					lowerCamelCase__		:   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):
										lowerCamelCase__		:   Union[str, Any]  				=					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 				__a       (			):







					"""simple docstring"""





					from timeit import timeit

					lowerCamelCase__		:   Any  				=					'''from __main__ import slow_primes, primes, fast_primes'''
					print(timeit('''slow_primes(1_000_000_000_000)'''							, setup=_lowercase							, number=1000000						)						)
					print(timeit('''primes(1_000_000_000_000)'''							, setup=_lowercase							, number=1000000						)						)
					print(timeit('''fast_primes(1_000_000_000_000)'''							, setup=_lowercase							, number=1000000						)						)


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







"""simple docstring"""




from transformers import HfArgumentParser, PyTorchBenchmark, PyTorchBenchmarkArguments



def 				__a       (			):







					"""simple docstring"""





					lowerCamelCase__		:   Union[str, Any]  				=					HfArgumentParser(_lowercase						)
					try:
										lowerCamelCase__		:   Optional[int]  				=					parser.parse_args_into_dataclasses()[0]
					except ValueError as e:
										lowerCamelCase__		:   Tuple  				=					'''Arg --no_{0} is no longer used, please use --no-{0} instead.'''
										lowerCamelCase__		:   Tuple  				=					''' '''.join(str(_lowercase						).split(''' '''						)[:-1]						)
										lowerCamelCase__		:   Union[str, Any]  				=					''''''
										lowerCamelCase__		:   int  				=					eval(str(_lowercase						).split(''' '''						)[-1]						)
										lowerCamelCase__		:   Any  				=					[]
										for arg in depreciated_args:
															# arg[2:] removes '--'
															if arg[2:] in PyTorchBenchmarkArguments.deprecated_args:
																				# arg[5:] removes '--no_'
																				full_error_msg += arg_error_msg.format(arg[5:]						)
															else:
																				wrong_args.append(_lowercase						)
										if len(_lowercase						) > 0:
															lowerCamelCase__		:   Any  				=					full_error_msg + begin_error_msg + str(_lowercase						)
										raise ValueError(_lowercase						)

					lowerCamelCase__		:   List[Any]  				=					PyTorchBenchmark(args=_lowercase						)
					benchmark.run()


if __name__ == "__main__":
					main()






