import random






def 							UpperCAmelCase__(					__UpperCAmelCase			:     int       ):
   __snake_case   :			Tuple										=						num - 1
   __snake_case   :			Dict										=						0

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

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






def 							UpperCAmelCase__(					__UpperCAmelCase			:     int       ):





   if num < 2:
      return False

   __snake_case   :			Dict										=						[
       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,
       1_01,
       1_03,
       1_07,
       1_09,
       1_13,
       1_27,
       1_31,
       1_37,
       1_39,
       1_49,
       1_51,
       1_57,
       1_63,
       1_67,
       1_73,
       1_79,
       1_81,
       1_91,
       1_93,
       1_97,
       1_99,
       2_11,
       2_23,
       2_27,
       2_29,
       2_33,
       2_39,
       2_41,
       2_51,
       2_57,
       2_63,
       2_69,
       2_71,
       2_77,
       2_81,
       2_83,
       2_93,
       3_07,
       3_11,
       3_13,
       3_17,
       3_31,
       3_37,
       3_47,
       3_49,
       3_53,
       3_59,
       3_67,
       3_73,
       3_79,
       3_83,
       3_89,
       3_97,
       4_01,
       4_09,
       4_19,
       4_21,
       4_31,
       4_33,
       4_39,
       4_43,
       4_49,
       4_57,
       4_61,
       4_63,
       4_67,
       4_79,
       4_87,
       4_91,
       4_99,
       5_03,
       5_09,
       5_21,
       5_23,
       5_41,
       5_47,
       5_57,
       5_63,
       5_69,
       5_71,
       5_77,
       5_87,
       5_93,
       5_99,
       6_01,
       6_07,
       6_13,
       6_17,
       6_19,
       6_31,
       6_41,
       6_43,
       6_47,
       6_53,
       6_59,
       6_61,
       6_73,
       6_77,
       6_83,
       6_91,
       7_01,
       7_09,
       7_19,
       7_27,
       7_33,
       7_39,
       7_43,
       7_51,
       7_57,
       7_61,
       7_69,
       7_73,
       7_87,
       7_97,
       8_09,
       8_11,
       8_21,
       8_23,
       8_27,
       8_29,
       8_39,
       8_53,
       8_57,
       8_59,
       8_63,
       8_77,
       8_81,
       8_83,
       8_87,
       9_07,
       9_11,
       9_19,
       9_29,
       9_37,
       9_41,
       9_47,
       9_53,
       9_67,
       9_71,
       9_77,
       9_83,
       9_91,
       9_97,
   ]

   if num in low_primes:
      return True

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

   return rabin_miller(SCREAMING_SNAKE_CASE_       )






def 							UpperCAmelCase__(					__UpperCAmelCase			:     int = 10_24       ):





   while True:
      __snake_case   :			Dict										=						random.randrange(2 ** (keysize - 1)     ,				2 ** (keysize)       )
      if is_prime_low_num(SCREAMING_SNAKE_CASE_       ):
         return num


if __name__ == "__main__":
 __magic_name__    							=							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


_SCREAMING_SNAKE_CASE									=				{
    "configuration_mctct": ["MCTCT_PRETRAINED_CONFIG_ARCHIVE_MAP", "MCTCTConfig"],
    "feature_extraction_mctct": ["MCTCTFeatureExtractor"],
    "processing_mctct": ["MCTCTProcessor"],
}


try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       _SCREAMING_SNAKE_CASE									=				[
           "MCTCT_PRETRAINED_MODEL_ARCHIVE_LIST",
           "MCTCTForCTC",
           "MCTCTModel",
           "MCTCTPreTrainedModel",
       ]


if TYPE_CHECKING:
       from .configuration_mctct import MCTCT_PRETRAINED_CONFIG_ARCHIVE_MAP, MCTCTConfig
       from .feature_extraction_mctct import MCTCTFeatureExtractor
       from .processing_mctct import MCTCTProcessor

       try:
              if not is_torch_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_mctct import MCTCT_PRETRAINED_MODEL_ARCHIVE_LIST, MCTCTForCTC, MCTCTModel, MCTCTPreTrainedModel

else:
       import sys

       _SCREAMING_SNAKE_CASE									=				_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)


