

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()



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
