





"""simple docstring"""




import random





def 						UpperCAmelCase__		(     _UpperCAmelCase					):






  """simple docstring"""





  A_  :       int										=  num - 1
  A_  :       List[str]										=  0

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

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





def 						UpperCAmelCase__		(     _UpperCAmelCase					):






  """simple docstring"""





  if num < 2:
    return False

  A_  :       str										=  [
      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 						UpperCAmelCase__		(     _UpperCAmelCase = 1024					):






  """simple docstring"""





  while True:
    A_  :       Union[str, Any]										=  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)))






"""simple docstring"""




def 						UpperCAmelCase__		(     _UpperCAmelCase					):






  """simple docstring"""





  A_  :       List[str]										=  hex_num.strip()
  if not hex_num:
    raise ValueError('No value was passed to the function'					)

  A_  :       Any										=  hex_num[0] == '-'
  if is_negative:
    A_  :       Optional[Any]										=  hex_num[1:]

  try:
    A_  :       Tuple										=  int(_UpperCAmelCase ,					16					)
  except ValueError:
    raise ValueError('Invalid value was passed to the function'					)

  A_  :       Union[str, Any]										=  ''
  while int_num > 0:
    A_  :       Optional[Any]										=  str(int_num % 2					) + bin_str
    int_num >>= 1

  return int(('-' + bin_str) if is_negative else bin_str					)


if __name__ == "__main__":
   import doctest

   doctest.testmod()