



'''simple docstring'''




import random



def      a      (			lowerCamelCase__   ):
			'''simple docstring'''





			A_     :						Tuple     =					num - 1
			A_     :						str     =					0

			while s % 2 == 0:
						A_     :						Tuple     =					s // 2
						t += 1

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



def      a      (			lowerCamelCase__   ):
			'''simple docstring'''





			if num < 2:
						return False

			A_     :						Optional[int]     =					[
			    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(_UpperCAmelCase   )



def      a      (			lowerCamelCase__ = 10_24   ):
			'''simple docstring'''





			while True:
						A_     :						Optional[int]     =					random.randrange(2 ** (keysize - 1)						,				2 ** (keysize)   )
						if is_prime_low_num(_UpperCAmelCase   ):
									return num


if __name__ == "__main__":
						lowerCamelCase							:Optional[int]     = 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


lowerCamelCase							:Dict       = {'''configuration_mmbt''': ['''MMBTConfig''']}

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCamelCase							:str       = ['''MMBTForClassification''', '''MMBTModel''', '''ModalEmbeddings''']


if TYPE_CHECKING:
						from .configuration_mmbt import MMBTConfig

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_mmbt import MMBTForClassification, MMBTModel, ModalEmbeddings

else:
						import sys

						lowerCamelCase							:Tuple       = _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)