





"""simple docstring"""
from ..utils import DummyObject, requires_backends






class       _SCREAMING_SNAKE_CASE(     metaclass=A						):
       SCREAMING_SNAKE_CASE_     :   Optional[Any]					=						['''torch''', '''transformers''', '''invisible_watermark''']




       def __init__(		self	,*SCREAMING_SNAKE_CASE__	,**SCREAMING_SNAKE_CASE__							)    ->   List[Any]:





             """simple docstring"""






             requires_backends(self	,['''torch''', '''transformers''', '''invisible_watermark''']							)




       @classmethod
       def 					_UpperCamelCase  (		cls	,*SCREAMING_SNAKE_CASE__	,**SCREAMING_SNAKE_CASE__							)    ->   int:





             """simple docstring"""






             requires_backends(cls	,['''torch''', '''transformers''', '''invisible_watermark''']							)




       @classmethod
       def 					_UpperCamelCase  (		cls	,*SCREAMING_SNAKE_CASE__	,**SCREAMING_SNAKE_CASE__							)    ->   Optional[Any]:





             """simple docstring"""






             requires_backends(cls	,['''torch''', '''transformers''', '''invisible_watermark''']							)






class       _SCREAMING_SNAKE_CASE(     metaclass=A						):
       SCREAMING_SNAKE_CASE_     :   Union[str, Any]					=						['''torch''', '''transformers''', '''invisible_watermark''']




       def __init__(		self	,*SCREAMING_SNAKE_CASE__	,**SCREAMING_SNAKE_CASE__							)    ->   List[Any]:





             """simple docstring"""






             requires_backends(self	,['''torch''', '''transformers''', '''invisible_watermark''']							)




       @classmethod
       def 					_UpperCamelCase  (		cls	,*SCREAMING_SNAKE_CASE__	,**SCREAMING_SNAKE_CASE__							)    ->   Union[str, Any]:





             """simple docstring"""






             requires_backends(cls	,['''torch''', '''transformers''', '''invisible_watermark''']							)




       @classmethod
       def 					_UpperCamelCase  (		cls	,*SCREAMING_SNAKE_CASE__	,**SCREAMING_SNAKE_CASE__							)    ->   Optional[int]:





             """simple docstring"""






             requires_backends(cls	,['''torch''', '''transformers''', '''invisible_watermark''']							)






"""simple docstring"""
import math
from collections.abc import Generator



def   __lowerCamelCase     (							a_  :	int							)    ->   Generator[int, None, None]:
      __SCREAMING_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				,     a_							):
                  if (i % j) == 0:
                        break
            else:
                  yield i



def   __lowerCamelCase     (							a_  :	int							)    ->   Generator[int, None, None]:
      __SCREAMING_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)
            __SCREAMING_SNAKE_CASE     :Tuple	       =						int(math.sqrt(a_							)							) + 1
            for j in range(2				,     a_							):
                  if (i % j) == 0:
                        break
            else:
                  yield i



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



def   __lowerCamelCase     (							)    ->   Union[str, Any]:
      from timeit import timeit

      __SCREAMING_SNAKE_CASE     :Optional[Any]	       =						'''from __main__ import slow_primes, primes, fast_primes'''
      print(timeit('''slow_primes(1_000_000_000_000)'''				,     setup=a_				,     number=1_00_00_00							)							)
      print(timeit('''primes(1_000_000_000_000)'''				,     setup=a_				,     number=1_00_00_00							)							)
      print(timeit('''fast_primes(1_000_000_000_000)'''				,     setup=a_				,     number=1_00_00_00							)							)


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