
"""simple docstring"""






import math
from collections.abc import Generator



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



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



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



def     lowerCAmelCase__ (		)	->str:
			from timeit import timeit

			__lowercase						      =					"from __main__ import slow_primes, primes, fast_primes"
			print(timeit("slow_primes(1_000_000_000_000)" ,      setup=__magic_name__ ,      number=1_0_0_0_0_0_0			)			)
			print(timeit("primes(1_000_000_000_000)" ,      setup=__magic_name__ ,      number=1_0_0_0_0_0_0			)			)
			print(timeit("fast_primes(1_000_000_000_000)" ,      setup=__magic_name__ ,      number=1_0_0_0_0_0_0			)			)


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







"""simple docstring"""






def     lowerCAmelCase__ (		__magic_name__ ,      __magic_name__			)	->list:
			__lowercase						      =					len(__magic_name__			)
			__lowercase						      =					len(__magic_name__			)
			__lowercase						      =					(
			    first_input_list_length
			    if first_input_list_length > second_input_list_length
			    else second_input_list_length
			)
			__lowercase						      =					[]
			for char_count in range(__magic_name__			):
						if char_count < first_input_list_length:
									output_result_list.append(first_input_list[char_count]			)
						if char_count < second_input_list_length:
									output_result_list.append(second_input_list[char_count]			)

			return output_result_list


if __name__ == "__main__":
					print(alternative_list_arrange(['''A''', '''B''', '''C'''], [1, 2, 3, 4, 5]), end=''' ''')





