'''simple docstring'''




import math

def 	UpperCamelCase_							(					_UpperCAmelCase  :      int    )    ->    bool:


       """simple docstring"""







       if 1 < number < 4:
              # 2 and 3 are primes
              return True
       elif number < 2 or number % 2 == 0 or number % 3 == 0:
              # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
              return False

       # All primes number are in format of 6k +/- 1
       for i in range(5			,	int(math.sqrt(_UpperCAmelCase    ) + 1    )			,	6    ):
              if number % i == 0 or number % (i + 2) == 0:
                     return False
       return True

def 	UpperCamelCase_							(					_UpperCAmelCase  :      float = 0.1    )    ->    int:


       """simple docstring"""







       _UpperCAmelCase     :  List[str]							      =    3
       _UpperCAmelCase     :  Union[str, Any]							      =    3

       while primes / (2 * j - 1) >= ratio:
              for i in range(j * j + j + 1			,	(j + 2) * (j + 2)			,	j + 1    ):
                     primes += is_prime(_UpperCAmelCase    )
              j += 2
       return j


if __name__ == "__main__":
  import doctest

  doctest.testmod()





from ...utils import (
    OptionalDependencyNotAvailable,
    is_torch_available,
    is_transformers_available,
    is_transformers_version,
)


try:
 if not (is_transformers_available() and is_torch_available()):
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 from ...utils.dummy_torch_and_transformers_objects import ShapEPipeline
else:
 from .camera import create_pan_cameras
 from .pipeline_shap_e import ShapEPipeline
 from .pipeline_shap_e_img2img import ShapEImgaImgPipeline
 from .renderer import (
     BoundingBoxVolume,
     ImportanceRaySampler,
     MLPNeRFModelOutput,
     MLPNeRSTFModel,
     ShapEParamsProjModel,
     ShapERenderer,
     StratifiedRaySampler,
     VoidNeRFModel,
 )


