
'''simple docstring'''




import random







def 						lowerCAmelCase_							(  snake_case__		):




    '''simple docstring'''



    A			:  Union[str, Any]   =		num - 1
    A			:  Union[str, Any]   =		0

    while s % 2 == 0:
        A			:  Optional[int]   =		s // 2
        t += 1

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







def 						lowerCAmelCase_							(  snake_case__		):




    '''simple docstring'''



    if num < 2:
        return False

    A			:  List[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(snake_case__		)







def 						lowerCAmelCase_							(  snake_case__ = 1024		):




    '''simple docstring'''



    while True:
        A			:  Union[str, Any]   =		random.randrange(2 ** (keysize - 1)						,							2 ** (keysize)		)
        if is_prime_low_num(snake_case__		):
            return num


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






'''simple docstring'''




from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


lowercase     :							Tuple       						=     {
    'configuration_luke': ['LUKE_PRETRAINED_CONFIG_ARCHIVE_MAP', 'LukeConfig'],
    'tokenization_luke': ['LukeTokenizer'],
}

try:
      if not is_torch_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      lowercase     :							int       						=     [
          'LUKE_PRETRAINED_MODEL_ARCHIVE_LIST',
          'LukeForEntityClassification',
          'LukeForEntityPairClassification',
          'LukeForEntitySpanClassification',
          'LukeForMultipleChoice',
          'LukeForQuestionAnswering',
          'LukeForSequenceClassification',
          'LukeForTokenClassification',
          'LukeForMaskedLM',
          'LukeModel',
          'LukePreTrainedModel',
      ]


if TYPE_CHECKING:
      from .configuration_luke import LUKE_PRETRAINED_CONFIG_ARCHIVE_MAP, LukeConfig
      from .tokenization_luke import LukeTokenizer

      try:
            if not is_torch_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_luke import (
                LUKE_PRETRAINED_MODEL_ARCHIVE_LIST,
                LukeForEntityClassification,
                LukeForEntityPairClassification,
                LukeForEntitySpanClassification,
                LukeForMaskedLM,
                LukeForMultipleChoice,
                LukeForQuestionAnswering,
                LukeForSequenceClassification,
                LukeForTokenClassification,
                LukeModel,
                LukePreTrainedModel,
            )

else:
      import sys

      lowercase     :							Dict       						=     _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)




