


import math
from collections.abc import Generator






def    _UpperCAmelCase	(   __lowerCamelCase       )		->Generator[int, None, None]:


 '''simple docstring'''
 snake_case   : 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 ,     __lowerCamelCase       ):
   if (i % j) == 0:
    break
  else:
   yield i






def    _UpperCAmelCase	(   __lowerCamelCase       )		->Generator[int, None, None]:


 '''simple docstring'''
 snake_case   : 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)
  snake_case   : Dict	  =      int(math.sqrt(__lowerCamelCase       )       ) + 1
  for j in range(2 ,     __lowerCamelCase       ):
   if (i % j) == 0:
    break
  else:
   yield i






def    _UpperCAmelCase	(   __lowerCamelCase       )		->Generator[int, None, None]:


 '''simple docstring'''
 snake_case   : 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):
  snake_case   : str	  =      int(math.sqrt(__lowerCamelCase       )       ) + 1
  for j in range(3 ,     __lowerCamelCase ,     2       ):
   # As we removed the even numbers, we don't need them now
   if (i % j) == 0:
    break
  else:
   yield i






def    _UpperCAmelCase	(   )		->Any:


 '''simple docstring'''
 from timeit import timeit

 snake_case   : Union[str, Any]	  =      '''from __main__ import slow_primes, primes, fast_primes'''
 print(timeit('''slow_primes(1_000_000_000_000)''' ,     setup=__lowerCamelCase ,     number=1000000       )       )
 print(timeit('''primes(1_000_000_000_000)''' ,     setup=__lowerCamelCase ,     number=1000000       )       )
 print(timeit('''fast_primes(1_000_000_000_000)''' ,     setup=__lowerCamelCase ,     number=1000000       )       )


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










from typing import Callable






def    _UpperCAmelCase	(   __lowerCamelCase       )		->Tuple:


 '''simple docstring'''

 def wrapper(__lowerCamelCase       ):
  snake_case   : str	  =      function_with_docstring.__doc__
  return target_function

 return wrapper






