'''simple docstring'''





import random



def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: int			)							->      bool:







  """simple docstring"""





  SCREAMING_SNAKE_CASE__    							=   num - 1
  SCREAMING_SNAKE_CASE__    							=   0

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

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



def 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: int			)							->      bool:







  """simple docstring"""





  if num < 2:
    return False

  SCREAMING_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,
      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 			__SCREAMING_SNAKE_CASE						(      __UpperCamelCase					: int = 10_24			)							->      int:







  """simple docstring"""





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


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

import pickle
import unittest

import torch

from accelerate import Accelerator
from accelerate.state import AcceleratorState
from accelerate.test_utils import require_cpu







@require_cpu
class __snake_case       (		unittest.TestCase	):




   def 			__a		(					self    :       Any   ):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__    							=   torch.nn.Linear(10 ,			10   )
     SCREAMING_SNAKE_CASE__    							=   torch.optim.SGD(model.parameters() ,			0.1   )
     SCREAMING_SNAKE_CASE__    							=   Accelerator()
     SCREAMING_SNAKE_CASE__    							=   accelerator.prepare(_lowercase   )
     try:
       pickle.loads(pickle.dumps(_lowercase   )   )
     except Exception as e:
       self.fail(f"""Accelerated optimizer pickling failed with {e}"""   )
     AcceleratorState._reset_state()
