



import math
from collections.abc import Generator


def 						UpperCAmelCase__   (   UpperCAmelCase__			:int       ):






 '''simple docstring'''

 a							=		(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 						UpperCAmelCase__   (   UpperCAmelCase__			:int       ):






 '''simple docstring'''

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


def 						UpperCAmelCase__   (   UpperCAmelCase__			:int       ):






 '''simple docstring'''

 a							=		(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):
  a							=		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 						UpperCAmelCase__   (   ):






 '''simple docstring'''

 from timeit import timeit

 a							=		"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__":
     A_		:  Tuple										=  int(input('''Calculate primes up to:\n>> ''').strip())
     for ret in primes(number):
          print(ret)
     benchmark()





def   snake_case_	(    snake_case	)    ->							str:
       lowercase__:  Optional[Any]         =  1
       lowercase__:  Optional[Any]         =  0
       lowercase__:  int         =  1
       lowercase__:  Any         =  1
       lowercase__:  Optional[Any]         =  3
       lowercase__:  List[str]         =  3
       lowercase__:  Optional[Any]         =  limit
       lowercase__:  List[Any]         =  0

       lowercase__:  int         =  ''
       while counter != decimal + 1:
              if 4 * q + r - t < n * t:
                     result += str(snake_case	)
                     if counter == 0:
                            result += "."

                     if decimal == counter:
                            break

                     counter += 1
                     lowercase__:  List[Any]         =  10 * (r - n * t)
                     lowercase__:  int         =  ((10 * (3 * q + r)) // t) - 10 * n
                     q *= 10
                     lowercase__:  Any         =  nr
              else:
                     lowercase__:  List[str]         =  (2 * q + r) * l
                     lowercase__:  Tuple         =  (q * (7 * k) + 2 + (r * l)) // (t * l)
                     q *= k
                     t *= l
                     l += 2
                     k += 1
                     lowercase__:  Dict         =  nn
                     lowercase__:  Optional[int]         =  nr
       return result




def   snake_case_	(    )    ->							None:
       print(f'{calculate_pi(50	) = }'	)
       import doctest

       doctest.testmod()


if __name__ == "__main__":
 main()


