

from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


lowerCamelCase      				=     {
    '''configuration_pegasus_x''': ['''PEGASUS_X_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''PegasusXConfig'''],
}

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  lowerCamelCase      				=     [
      '''PEGASUS_X_PRETRAINED_MODEL_ARCHIVE_LIST''',
      '''PegasusXForConditionalGeneration''',
      '''PegasusXModel''',
      '''PegasusXPreTrainedModel''',
  ]


if TYPE_CHECKING:
  from .configuration_pegasus_x import PEGASUS_X_PRETRAINED_CONFIG_ARCHIVE_MAP, PegasusXConfig

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_pegasus_x import (
        PEGASUS_X_PRETRAINED_MODEL_ARCHIVE_LIST,
        PegasusXForConditionalGeneration,
        PegasusXModel,
        PegasusXPreTrainedModel,
    )


else:
  import sys

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









import random


def        __lowercase    (  UpperCAmelCase__      ):

					"""simple docstring"""






					__lowerCAmelCase					=							num - 1
					__lowerCAmelCase					=							0

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

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


def        __lowercase    (  UpperCAmelCase__      ):

					"""simple docstring"""






					if num < 2:
										return False

					__lowerCAmelCase					=							[
					    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(UpperCAmelCase__      )


def        __lowercase    (  UpperCAmelCase__ = 1_024      ):

					"""simple docstring"""






					while True:
										__lowerCAmelCase					=							random.randrange(2 ** (keysize - 1)		,					2 ** (keysize)      )
										if is_prime_low_num(UpperCAmelCase__      ):
															return num


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






