





'''simple docstring'''






import os

from packaging import version

from .. import __version__
from .accelerate_utils import apply_forward_hook
from .constants import (
    CONFIG_NAME,
    DEPRECATED_REVISION_ARGS,
    DIFFUSERS_CACHE,
    DIFFUSERS_DYNAMIC_MODULE_NAME,
    FLAX_WEIGHTS_NAME,
    HF_MODULES_CACHE,
    HUGGINGFACE_CO_RESOLVE_ENDPOINT,
    ONNX_EXTERNAL_WEIGHTS_NAME,
    ONNX_WEIGHTS_NAME,
    SAFETENSORS_WEIGHTS_NAME,
    TEXT_ENCODER_ATTN_MODULE,
    WEIGHTS_NAME,
)
from .deprecation_utils import deprecate
from .doc_utils import replace_example_docstring
from .dynamic_modules_utils import get_class_from_dynamic_module
from .hub_utils import (
    HF_HUB_OFFLINE,
    _add_variant,
    _get_model_file,
    extract_commit_hash,
    http_user_agent,
)
from .import_utils import (
    BACKENDS_MAPPING,
    ENV_VARS_TRUE_AND_AUTO_VALUES,
    ENV_VARS_TRUE_VALUES,
    USE_JAX,
    USE_TF,
    USE_TORCH,
    DummyObject,
    OptionalDependencyNotAvailable,
    is_accelerate_available,
    is_accelerate_version,
    is_bsa_available,
    is_flax_available,
    is_ftfy_available,
    is_inflect_available,
    is_invisible_watermark_available,
    is_k_diffusion_available,
    is_k_diffusion_version,
    is_librosa_available,
    is_note_seq_available,
    is_omegaconf_available,
    is_onnx_available,
    is_safetensors_available,
    is_scipy_available,
    is_tensorboard_available,
    is_tf_available,
    is_torch_available,
    is_torch_version,
    is_torchsde_available,
    is_transformers_available,
    is_transformers_version,
    is_unidecode_available,
    is_wandb_available,
    is_xformers_available,
    requires_backends,
)
from .logging import get_logger
from .outputs import BaseOutput
from .pil_utils import PIL_INTERPOLATION, numpy_to_pil, pt_to_pil
from .torch_utils import is_compiled_module, randn_tensor


if is_torch_available():
		from .testing_utils import (
		    floats_tensor,
		    load_hf_numpy,
		    load_image,
		    load_numpy,
		    load_pt,
		    nightly,
		    parse_flag_from_env,
		    print_tensor_test,
		    require_torch_a,
		    require_torch_gpu,
		    skip_mps,
		    slow,
		    torch_all_close,
		    torch_device,
		)
		from .torch_utils import maybe_allow_in_graph

from .testing_utils import export_to_gif, export_to_video


A :			List[Any]							   =      get_logger(__name__)





def    lowercase_   (		lowercase__    ) ->Optional[int]:
						if version.parse(lowercase__    ) < version.parse(lowercase__    ):
												if "dev" in min_version:
																		_snake_case: int	       =		(
																		    'This example requires a source install from HuggingFace diffusers (see '
																		    '`https://huggingface.co/docs/diffusers/installation#install-from-source`),'
																		)
												else:
																		_snake_case: List[str]	       =		F'''This example requires a minimum version of {min_version},'''
												error_message += F''' but the version found is {__version__}.\n'''
												raise ImportError(lowercase__    )












'''simple docstring'''






import math
from collections.abc import Generator





def    lowercase_   (		lowercase__    ) ->Generator[int, None, None]:
						_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					,	lowercase__    ):
																		if (i % j) == 0:
																								break
												else:
																		yield i





def    lowercase_   (		lowercase__    ) ->Generator[int, None, None]:
						_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)
												_snake_case: int	       =		int(math.sqrt(lowercase__    )    ) + 1
												for j in range(2					,	lowercase__    ):
																		if (i % j) == 0:
																								break
												else:
																		yield i





def    lowercase_   (		lowercase__    ) ->Generator[int, None, None]:
						_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):
												_snake_case: List[str]	       =		int(math.sqrt(lowercase__    )    ) + 1
												for j in range(3					,	lowercase__					,	2    ):
																		# As we removed the even numbers, we don't need them now
																		if (i % j) == 0:
																								break
												else:
																		yield i





def    lowercase_   (		) ->Optional[int]:
						from timeit import timeit

						_snake_case: Dict	       =		'from __main__ import slow_primes, primes, fast_primes'
						print(timeit('slow_primes(1_000_000_000_000)'					,	setup=lowercase__					,	number=100_0000    )    )
						print(timeit('primes(1_000_000_000_000)'					,	setup=lowercase__					,	number=100_0000    )    )
						print(timeit('fast_primes(1_000_000_000_000)'					,	setup=lowercase__					,	number=100_0000    )    )


if __name__ == "__main__":
		A :			List[str]							   =      int(input('Calculate primes up to:\n>> ').strip())
		for ret in primes(number):
				print(ret)
		benchmark()





