code: 
  
  import math
  from collections.abc import Generator
  
  
  
  
  def     UpperCAmelCase__       (    _A   :				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			,   _A							):
        if (i % j) == 0:
          break
      else:
        yield i
  
  
  
  
  def     UpperCAmelCase__       (    _A   :				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(_A							)							) + 1
      for j in range(2			,   _A							):
        if (i % j) == 0:
          break
      else:
        yield i
  
  
  
  
  def     UpperCAmelCase__       (    _A   :				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(_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     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=_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()
  
style_context: 
  
  from dataclasses import dataclass
  from typing import List, Optional, Union
  
  import numpy as np
  import PIL
  from PIL import Image
  
  from ...utils import BaseOutput, is_torch_available, is_transformers_available
  
  
  
  
  
  
  
  @dataclass
  # Copied from diffusers.pipelines.stable_diffusion.__init__.StableDiffusionPipelineOutput with Stable->Alt
  class 		__magic_name__    (							lowerCamelCase__							):
  
     '''simple docstring'''
  
  
  
  
     lowerCamelCase__				:			Union[List[PIL.Image.Image], np.ndarray]
     lowerCamelCase__				:			Optional[List[bool]]
  
  
  if is_transformers_available() and is_torch_available():
         from .modeling_roberta_series import RobertaSeriesModelWithTransformation
         from .pipeline_alt_diffusion import AltDiffusionPipeline
         from .pipeline_alt_diffusion_imgaimg import AltDiffusionImgaImgPipeline
  