


import random






def 	__lowerCAmelCase      (SCREAMING_SNAKE_CASE )->  bool:




      """simple docstring"""

      snake_case_	=				num - 1
      snake_case_	=				0

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

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






def 	__lowerCAmelCase      (SCREAMING_SNAKE_CASE )->  bool:




      """simple docstring"""

      if num < 2:
            return False

      snake_case_	=				[
          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(SCREAMING_SNAKE_CASE )






def 	__lowerCAmelCase      (SCREAMING_SNAKE_CASE = 1024 )->  int:




      """simple docstring"""

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


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



from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


UpperCAmelCase      =   {"""configuration_vit_msn""": ["""VIT_MSN_PRETRAINED_CONFIG_ARCHIVE_MAP""", """ViTMSNConfig"""]}

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCAmelCase      =   [
       """VIT_MSN_PRETRAINED_MODEL_ARCHIVE_LIST""",
       """ViTMSNModel""",
       """ViTMSNForImageClassification""",
       """ViTMSNPreTrainedModel""",
   ]

if TYPE_CHECKING:
   from .configuration_vit_msn import VIT_MSN_PRETRAINED_CONFIG_ARCHIVE_MAP, ViTMSNConfig

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_vit_msn import (
          VIT_MSN_PRETRAINED_MODEL_ARCHIVE_LIST,
          ViTMSNForImageClassification,
          ViTMSNModel,
          ViTMSNPreTrainedModel,
      )

else:
   import sys

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