
import random


def     __lowerCAmelCase			(			a__  )       ->  bool:
				__a										=    num - 1
				__a										=    0

				while s % 2 == 0:
								__a										=    s // 2
								t += 1

				for _ in range(5  ):
								__a										=    random.randrange(2						,    num - 1  )
								__a										=    pow(a__						,    a__						,    a__  )
								if v != 1:
												__a										=    0
												while v != (num - 1):
																if i == t - 1:
																				return False
																else:
																				__a										=    i + 1
																				__a										=    (v**2) % num
				return True


def     __lowerCAmelCase			(			a__  )       ->  bool:
				if num < 2:
								return False

				__a										=    [
				    2,
				    3,
				    5,
				    7,
				    11,
				    13,
				    17,
				    19,
				    23,
				    29,
				    31,
				    37,
				    41,
				    43,
				    47,
				    53,
				    59,
				    61,
				    67,
				    71,
				    73,
				    79,
				    83,
				    89,
				    97,
				    101,
				    103,
				    107,
				    109,
				    113,
				    127,
				    131,
				    137,
				    139,
				    149,
				    151,
				    157,
				    163,
				    167,
				    173,
				    179,
				    181,
				    191,
				    193,
				    197,
				    199,
				    211,
				    223,
				    227,
				    229,
				    233,
				    239,
				    241,
				    251,
				    257,
				    263,
				    269,
				    271,
				    277,
				    281,
				    283,
				    293,
				    307,
				    311,
				    313,
				    317,
				    331,
				    337,
				    347,
				    349,
				    353,
				    359,
				    367,
				    373,
				    379,
				    383,
				    389,
				    397,
				    401,
				    409,
				    419,
				    421,
				    431,
				    433,
				    439,
				    443,
				    449,
				    457,
				    461,
				    463,
				    467,
				    479,
				    487,
				    491,
				    499,
				    503,
				    509,
				    521,
				    523,
				    541,
				    547,
				    557,
				    563,
				    569,
				    571,
				    577,
				    587,
				    593,
				    599,
				    601,
				    607,
				    613,
				    617,
				    619,
				    631,
				    641,
				    643,
				    647,
				    653,
				    659,
				    661,
				    673,
				    677,
				    683,
				    691,
				    701,
				    709,
				    719,
				    727,
				    733,
				    739,
				    743,
				    751,
				    757,
				    761,
				    769,
				    773,
				    787,
				    797,
				    809,
				    811,
				    821,
				    823,
				    827,
				    829,
				    839,
				    853,
				    857,
				    859,
				    863,
				    877,
				    881,
				    883,
				    887,
				    907,
				    911,
				    919,
				    929,
				    937,
				    941,
				    947,
				    953,
				    967,
				    971,
				    977,
				    983,
				    991,
				    997,
				]

				if num in low_primes:
								return True

				for prime in low_primes:
								if (num % prime) == 0:
												return False

				return rabin_miller(a__  )


def     __lowerCAmelCase			(			a__ = 1024  )       ->  int:
				while True:
								__a										=    random.randrange(2 ** (keysize - 1)						,    2 ** (keysize)  )
								if is_prime_low_num(a__  ):
												return num


if __name__ == "__main__":
					A     :	Any    = generate_large_prime()
					print(('Prime number:', num))
					print(('is_prime_low_num:', is_prime_low_num(num)))







__UpperCAmelCase								=						{
    'Pillow': 'Pillow<10.0.0',
    'accelerate': 'accelerate>=0.20.3',
    'av': 'av==9.2.0',
    'beautifulsoup4': 'beautifulsoup4',
    'black': 'black~=23.1',
    'codecarbon': 'codecarbon==1.2.0',
    'cookiecutter': 'cookiecutter==1.7.3',
    'dataclasses': 'dataclasses',
    'datasets': 'datasets!=2.5.0',
    'decord': 'decord==0.6.0',
    'deepspeed': 'deepspeed>=0.9.3',
    'diffusers': 'diffusers',
    'dill': 'dill<0.3.5',
    'evaluate': 'evaluate>=0.2.0',
    'fairscale': 'fairscale>0.3',
    'faiss-cpu': 'faiss-cpu',
    'fastapi': 'fastapi',
    'filelock': 'filelock',
    'flax': 'flax>=0.4.1,<=0.7.0',
    'ftfy': 'ftfy',
    'fugashi': 'fugashi>=1.0',
    'GitPython': 'GitPython<3.1.19',
    'hf-doc-builder': 'hf-doc-builder>=0.3.0',
    'huggingface-hub': 'huggingface-hub>=0.14.1,<1.0',
    'importlib_metadata': 'importlib_metadata',
    'ipadic': 'ipadic>=1.0.0,<2.0',
    'isort': 'isort>=5.5.4',
    'jax': 'jax>=0.2.8,!=0.3.2,<=0.4.13',
    'jaxlib': 'jaxlib>=0.1.65,<=0.4.13',
    'jieba': 'jieba',
    'kenlm': 'kenlm',
    'keras-nlp': 'keras-nlp>=0.3.1',
    'librosa': 'librosa',
    'nltk': 'nltk',
    'natten': 'natten>=0.14.6',
    'numpy': 'numpy>=1.17',
    'onnxconverter-common': 'onnxconverter-common',
    'onnxruntime-tools': 'onnxruntime-tools>=1.4.2',
    'onnxruntime': 'onnxruntime>=1.4.0',
    'opencv-python': 'opencv-python',
    'optuna': 'optuna',
    'optax': 'optax>=0.0.8,<=0.1.4',
    'packaging': 'packaging>=20.0',
    'parameterized': 'parameterized',
    'phonemizer': 'phonemizer',
    'protobuf': 'protobuf',
    'psutil': 'psutil',
    'pyyaml': 'pyyaml>=5.1',
    'pydantic': 'pydantic<2',
    'pytest': 'pytest>=7.2.0',
    'pytest-timeout': 'pytest-timeout',
    'pytest-xdist': 'pytest-xdist',
    'python': 'python>=3.8.0',
    'ray[tune]': 'ray[tune]',
    'regex': 'regex!=2019.12.17',
    'requests': 'requests',
    'rhoknp': 'rhoknp>=1.1.0,<1.3.1',
    'rjieba': 'rjieba',
    'rouge-score': 'rouge-score!=0.0.7,!=0.0.8,!=0.1,!=0.1.1',
    'ruff': 'ruff>=0.0.241,<=0.0.259',
    'sacrebleu': 'sacrebleu>=1.4.12,<2.0.0',
    'sacremoses': 'sacremoses',
    'safetensors': 'safetensors>=0.3.1',
    'sagemaker': 'sagemaker>=2.31.0',
    'scikit-learn': 'scikit-learn',
    'sentencepiece': 'sentencepiece>=0.1.91,!=0.1.92',
    'sigopt': 'sigopt',
    'starlette': 'starlette',
    'sudachipy': 'sudachipy>=0.6.6',
    'sudachidict_core': 'sudachidict_core>=20220729',
    'tensorflow-cpu': 'tensorflow-cpu>=2.6,<2.14',
    'tensorflow': 'tensorflow>=2.6,<2.14',
    'tensorflow-text': 'tensorflow-text<2.14',
    'tf2onnx': 'tf2onnx',
    'timeout-decorator': 'timeout-decorator',
    'timm': 'timm',
    'tokenizers': 'tokenizers>=0.11.1,!=0.11.3,<0.14',
    'torch': 'torch>=1.9,!=1.12.0',
    'torchaudio': 'torchaudio',
    'torchvision': 'torchvision',
    'pyctcdecode': 'pyctcdecode>=0.4.0',
    'tqdm': 'tqdm>=4.27',
    'unidic': 'unidic>=1.0.2',
    'unidic_lite': 'unidic_lite>=1.0.7',
    'urllib3': 'urllib3<2.0.0',
    'uvicorn': 'uvicorn',
}






