code: 
  '''simple docstring'''
  
  
  
  
  
  import math
  from collections.abc import Generator
  
  
  def 				UpperCamelCase	(  snake_case   ):
  
  
  
  
     '''simple docstring'''
  
     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	,     snake_case   ):
           if (i % j) == 0:
              break
        else:
           yield i
  
  
  def 				UpperCamelCase	(  snake_case   ):
  
  
  
  
     '''simple docstring'''
  
     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(snake_case   )   ) + 1
        for j in range(2	,     snake_case   ):
           if (i % j) == 0:
              break
        else:
           yield i
  
  
  def 				UpperCamelCase	(  snake_case   ):
  
  
  
  
     '''simple docstring'''
  
     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__			:				List[str]       						= int(math.sqrt(snake_case   )   ) + 1
        for j in range(3	,     snake_case	,     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
  
     SCREAMING_SNAKE_CASE__			:				Dict       						= '''from __main__ import slow_primes, primes, fast_primes'''
     print(timeit('''slow_primes(1_000_000_000_000)'''	,     setup=snake_case	,     number=1_00_00_00   )   )
     print(timeit('''primes(1_000_000_000_000)'''	,     setup=snake_case	,     number=1_00_00_00   )   )
     print(timeit('''fast_primes(1_000_000_000_000)'''	,     setup=snake_case	,     number=1_00_00_00   )   )
  
  
  if __name__ == "__main__":
         lowercase__			=	int(input('''Calculate primes up to:\n>> ''').strip())
         for ret in primes(number):
                print(ret)
         benchmark()
  
  
style_context: 
  
  
  
  
  '''simple docstring'''
  
  
  
  
  
  # Copyright 2023 The HuggingFace Team. All rights reserved.
  #
  # Licensed under the Apache License, Version 2.0 (the "License");
  # you may not use this file except in compliance with the License.
  # You may obtain a copy of the License at
  #
  #     http://www.apache.org/licenses/LICENSE-2.0
  #
  # Unless required by applicable law or agreed to in writing, software
  # distributed under the License is distributed on an "AS IS" BASIS,
  # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  # See the License for the specific language governing permissions and
  # limitations under the License.
  from typing import TYPE_CHECKING
  
  # rely on isort to merge the imports
  from ...utils import (
      OptionalDependencyNotAvailable,
      _LazyModule,
      is_torch_available,
  )
  
  
  lowercase__			=	{
      '''configuration_convnextv2''': [
          '''CONVNEXTV2_PRETRAINED_CONFIG_ARCHIVE_MAP''',
          '''ConvNextV2Config''',
      ]
  }
  
  try:
         if not is_torch_available():
                raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
         pass
  else:
         lowercase__			=	[
             '''CONVNEXTV2_PRETRAINED_MODEL_ARCHIVE_LIST''',
             '''ConvNextV2ForImageClassification''',
             '''ConvNextV2Model''',
             '''ConvNextV2PreTrainedModel''',
             '''ConvNextV2Backbone''',
         ]
  
  
  if TYPE_CHECKING:
         from .configuration_convnextva import (
             CONVNEXTV2_PRETRAINED_CONFIG_ARCHIVE_MAP,
             ConvNextVaConfig,
         )
  
         try:
                if not is_torch_available():
                       raise OptionalDependencyNotAvailable()
         except OptionalDependencyNotAvailable:
                pass
         else:
                from .modeling_convnextva import (
                    CONVNEXTV2_PRETRAINED_MODEL_ARCHIVE_LIST,
                    ConvNextVaBackbone,
                    ConvNextVaForImageClassification,
                    ConvNextVaModel,
                    ConvNextVaPreTrainedModel,
                )
  
  else:
         import sys
  
         lowercase__			=	_LazyModule(__name__, globals()['''__file__'''], _import_structure)
  
  