

"""simple docstring"""



from __future__ import annotations

import math





def  _snake_case     (    UpperCAmelCase_  :					int			):

     if 1 < number < 4:
          # 2 and 3 are primes
          return True
     elif number < 2 or number % 2 == 0 or number % 3 == 0:
          # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
          return False

     # All primes number are in format of 6k +/- 1
     for i in range(5					,   int(math.sqrt(UpperCAmelCase_			) + 1			)					,   6			):
          if number % i == 0 or number % (i + 2) == 0:
               return False
     return True





def  _snake_case     (    UpperCAmelCase_  :					int			):
     A__										=  str(UpperCAmelCase_			)
     A__										=  [n]
     for i in range(1					,   len(UpperCAmelCase_			)			):
          list_nums.append(int(str_num[i:]			)			)
          list_nums.append(int(str_num[:-i]			)			)
     return list_nums





def  _snake_case     (    UpperCAmelCase_  :					int			):
     if len(str(UpperCAmelCase_			)			) > 3:
          if not is_prime(int(str(UpperCAmelCase_			)[-3:]			)			) or not is_prime(int(str(UpperCAmelCase_			)[:3]			)			):
               return False
     return True





def  _snake_case     (    UpperCAmelCase_  :					int = 11			):
     A__										=  []
     A__										=  13
     while len(UpperCAmelCase_			) != count:
          if validate(UpperCAmelCase_			):
               A__										=  list_truncated_nums(UpperCAmelCase_			)
               if all(is_prime(UpperCAmelCase_			) for i in list_nums			):
                    list_truncated_primes.append(UpperCAmelCase_			)
          num += 2
     return list_truncated_primes





def  _snake_case     (    ):
     return sum(compute_truncated_primes(11			)			)


if __name__ == "__main__":
 print(f"""{sum(compute_truncated_primes(1_1)) = }""")









"""simple docstring"""



SCREAMING_SNAKE_CASE_					:	str							  =						'0.21.0'

from .accelerator import Accelerator
from .big_modeling import (
    cpu_offload,
    cpu_offload_with_hook,
    disk_offload,
    dispatch_model,
    init_empty_weights,
    init_on_device,
    load_checkpoint_and_dispatch,
)
from .data_loader import skip_first_batches
from .launchers import debug_launcher, notebook_launcher
from .state import PartialState
from .utils import (
    DeepSpeedPlugin,
    DistributedDataParallelKwargs,
    DistributedType,
    FullyShardedDataParallelPlugin,
    GradScalerKwargs,
    InitProcessGroupKwargs,
    find_executable_batch_size,
    infer_auto_device_map,
    is_rich_available,
    load_checkpoint_in_model,
    synchronize_rng_states,
)


if is_rich_available():
 from .utils import rich






