

'''simple docstring'''

import random




def 				UpperCamelCase(					UpperCAmelCase_     ):
 UpperCAmelCase	:     List[Any]						 =			num - 1
 UpperCAmelCase	:     Optional[int]						 =			0

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

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




def 				UpperCamelCase(					UpperCAmelCase_     ):


 if num < 2:
  return False

 UpperCAmelCase	:     Optional[Any]						 =			[
     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(lowerCAmelCase__     )




def 				UpperCamelCase(					UpperCAmelCase_ = 10_24     ):


 while True:
  UpperCAmelCase	:     Union[str, Any]						 =			random.randrange(2 ** (keysize - 1)  ,	2 ** (keysize)     )
  if is_prime_low_num(lowerCAmelCase__     ):
   return num


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







'''simple docstring'''

# Lint as: python3
import itertools
import os
import re


lowercase__         =      re.compile(r"([A-Z]+)([A-Z][a-z])")
lowercase__         =      re.compile(r"([a-z\d])([A-Z])")

lowercase__         =      re.compile(r"(?<!_)_(?!_)")
lowercase__         =      re.compile(r"(_{2,})")

lowercase__         =      r"^\w+(\.\w+)*$"

lowercase__         =      r"<>:/\|?*"




def 				UpperCamelCase(					UpperCAmelCase_     ):
 UpperCAmelCase	:     List[str]						 =			_uppercase_uppercase_re.sub(R'\1_\2'  ,	UpperCAmelCase_     )
 UpperCAmelCase	:     str						 =			_lowercase_uppercase_re.sub(R'\1_\2'  ,	UpperCAmelCase_     )
 return name.lower()




def 				UpperCamelCase(					UpperCAmelCase_     ):
 UpperCAmelCase	:     List[str]						 =			_single_underscore_re.split(UpperCAmelCase_     )
 UpperCAmelCase	:     Optional[Any]						 =			[_multiple_underscores_re.split(UpperCAmelCase_     ) for n in name]
 return "".join(n.capitalize() for n in itertools.chain.from_iterable(UpperCAmelCase_     ) if n != ''     )




def 				UpperCamelCase(					UpperCAmelCase_     ):
 if os.path.basename(UpperCAmelCase_     ) != name:
  raise ValueError(F"""Should be a dataset name, not a path: {name}"""     )
 return camelcase_to_snakecase(UpperCAmelCase_     )




def 				UpperCamelCase(					UpperCAmelCase_  ,	UpperCAmelCase_     ):
 if os.path.basename(UpperCAmelCase_     ) != name:
  raise ValueError(F"""Should be a dataset name, not a path: {name}"""     )
 if not re.match(_split_re  ,	UpperCAmelCase_     ):
  raise ValueError(F"""Split name should match '{_split_re}'' but got '{split}'."""     )
 return F"""{filename_prefix_for_name(UpperCAmelCase_     )}-{split}"""




def 				UpperCamelCase(					UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_=None     ):
 UpperCAmelCase	:     Dict						 =			filename_prefix_for_split(UpperCAmelCase_  ,	UpperCAmelCase_     )
 if filetype_suffix:
  prefix += F""".{filetype_suffix}"""
 UpperCAmelCase	:     Optional[int]						 =			os.path.join(UpperCAmelCase_  ,	UpperCAmelCase_     )
 return F"""{filepath}*"""




def 				UpperCamelCase(					UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_=None  ,	UpperCAmelCase_=None     ):
 UpperCAmelCase	:     Optional[int]						 =			filename_prefix_for_split(UpperCAmelCase_  ,	UpperCAmelCase_     )
 UpperCAmelCase	:     str						 =			os.path.join(UpperCAmelCase_  ,	UpperCAmelCase_     )

 if shard_lengths:
  UpperCAmelCase	:     List[str]						 =			len(UpperCAmelCase_     )
  UpperCAmelCase	:     List[str]						 =			[F"""{prefix}-{shard_id:05d}-of-{num_shards:05d}""" for shard_id in range(UpperCAmelCase_     )]
  if filetype_suffix:
   UpperCAmelCase	:     Dict						 =			[filename + F""".{filetype_suffix}""" for filename in filenames]
  return filenames
 else:
  UpperCAmelCase	:     Optional[Any]						 =			prefix
  if filetype_suffix:
   filename += F""".{filetype_suffix}"""
  return [filename]




