"""simple docstring"""
import math





def    lowerCAmelCase__    (			_UpperCamelCase       :				Optional[int]					)					->				Union[str, Any]:





						"""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(lowerCAmelCase__					) + 1					) ,			6					):
												if number % i == 0 or number % (i + 2) == 0:
																		return False
						return True





def    lowerCAmelCase__    (			_UpperCamelCase       :				int = 0.1					)					->				str:





						"""simple docstring"""






						snake_case								=			3
						snake_case								=			3

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


if __name__ == "__main__":
					import doctest

					doctest.testmod()







"""simple docstring"""
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,
					)


