

import random



def   __UpperCAmelCase					(      __a :     int      )     ->	bool:

					"""simple docstring"""

					_a      :       str   =						num - 1
					_a      :       Dict   =						0

					while s % 2 == 0:
										_a      :       Dict   =						s // 2
										t += 1

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



def   __UpperCAmelCase					(      __a :     int      )     ->	bool:

					"""simple docstring"""

					if num < 2:
										return False

					_a      :       str   =						[
					    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   __UpperCAmelCase					(      __a :     int = 1_024      )     ->	int:

					"""simple docstring"""

					while True:
										_a      :       List[Any]   =						random.randrange(2 ** (keysize - 1)						,2 ** (keysize)      )
										if is_prime_low_num(__a      ):
															return num


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







# flake8: noqa
# Lint as: python3

from typing import Dict, List, Optional, Type

from .. import config
from ..utils import logging
from .formatting import (
    ArrowFormatter,
    CustomFormatter,
    Formatter,
    PandasFormatter,
    PythonFormatter,
    TensorFormatter,
    format_table,
    query_table,
)
from .np_formatter import NumpyFormatter


A				:       Union[str, Any]      =  logging.get_logger(__name__)

A				:       Dict[Optional[str], Type[Formatter]]      =  {}
A				:       Dict[Optional[str], str]      =  {}
A				:       Dict[Optional[str], Exception]      =  {}





def 						_lowerCAmelCase							(     _lowerCAmelCase   ,						_lowerCAmelCase   ,						_lowerCAmelCase = None   ,						)    ->						str:


						'''simple docstring'''






						__snake_case				=		aliases if aliases is not None else []
						if format_type in _FORMAT_TYPES:
												logger.warning(
												    F'''Overwriting format type \'{format_type}\' ({_FORMAT_TYPES[format_type].__name__} -> {formatter_cls.__name__})'''			)
						__snake_case				=		formatter_cls
						for alias in set(aliases + [format_type]			):
												if alias in _FORMAT_TYPES_ALIASES:
																		logger.warning(
																		    F'''Overwriting format type alias \'{alias}\' ({_FORMAT_TYPES_ALIASES[alias]} -> {format_type})'''			)
												__snake_case				=		format_type





def 						_lowerCAmelCase							(     _lowerCAmelCase   ,						_lowerCAmelCase   ,						_lowerCAmelCase = None			)    ->						List[Any]:


						'''simple docstring'''






						__snake_case				=		aliases if aliases is not None else []
						for alias in set(aliases + [format_type]			):
												__snake_case				=		unavailable_error


# Here we define all the available formatting functions that can be used by `Dataset.set_format`
_register_formatter(PythonFormatter, None, aliases=['python'])
_register_formatter(ArrowFormatter, 'arrow', aliases=['pa', 'pyarrow'])
_register_formatter(NumpyFormatter, 'numpy', aliases=['np'])
_register_formatter(PandasFormatter, 'pandas', aliases=['pd'])
_register_formatter(CustomFormatter, 'custom')

if config.TORCH_AVAILABLE:
	from .torch_formatter import TorchFormatter

	_register_formatter(TorchFormatter, 'torch', aliases=['pt', 'pytorch'])
else:
	A				:       Any      =  ValueError('PyTorch needs to be installed to be able to return PyTorch tensors.')
	_register_unavailable_formatter(_torch_error, 'torch', aliases=['pt', 'pytorch'])

if config.TF_AVAILABLE:
	from .tf_formatter import TFFormatter

	_register_formatter(TFFormatter, 'tensorflow', aliases=['tf'])
else:
	A				:       Tuple      =  ValueError('Tensorflow needs to be installed to be able to return Tensorflow tensors.')
	_register_unavailable_formatter(_tf_error, 'tensorflow', aliases=['tf'])

if config.JAX_AVAILABLE:
	from .jax_formatter import JaxFormatter

	_register_formatter(JaxFormatter, 'jax', aliases=[])
else:
	A				:       Optional[int]      =  ValueError('JAX needs to be installed to be able to return JAX arrays.')
	_register_unavailable_formatter(_jax_error, 'jax', aliases=[])





def 						_lowerCAmelCase							(     _lowerCAmelCase			)    ->						Optional[str]:


						'''simple docstring'''






						if format_type in _FORMAT_TYPES_ALIASES:
												return _FORMAT_TYPES_ALIASES[format_type]
						else:
												return format_type





def 						_lowerCAmelCase							(     _lowerCAmelCase   ,						**_lowerCAmelCase			)    ->						Formatter:


						'''simple docstring'''






						__snake_case				=		get_format_type_from_alias(_lowerCAmelCase			)
						if format_type in _FORMAT_TYPES:
												return _FORMAT_TYPES[format_type](**_lowerCAmelCase			)
						if format_type in _FORMAT_TYPES_ALIASES_UNAVAILABLE:
												raise _FORMAT_TYPES_ALIASES_UNAVAILABLE[format_type]
						else:
												raise ValueError(
												    F'''Return type should be None or selected in {list(type for type in _FORMAT_TYPES.keys() if type != None			)}, but got \'{format_type}\''''			)





