


"""simple docstring"""







from __future__ import annotations

import math
def 					a__			(				SCREAMING_SNAKE_CASE    :    int				):


  '''simple docstring'''







  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(SCREAMING_SNAKE_CASE				) + 1				)				,      6				):
    if number % i == 0 or number % (i + 2) == 0:
      return False
  return True
def 					a__			(				SCREAMING_SNAKE_CASE    :    int				):


  '''simple docstring'''







  lowerCAmelCase     :     List[str]								=							str(SCREAMING_SNAKE_CASE				)
  lowerCAmelCase     :     Dict								=							[n]
  for i in range(1				,      len(SCREAMING_SNAKE_CASE				)				):
    list_nums.append(int(str_num[i:]				)				)
    list_nums.append(int(str_num[:-i]				)				)
  return list_nums
def 					a__			(				SCREAMING_SNAKE_CASE    :    int				):


  '''simple docstring'''







  if len(str(SCREAMING_SNAKE_CASE				)				) > 3:
    if not is_prime(int(str(SCREAMING_SNAKE_CASE				)[-3:]				)				) or not is_prime(int(str(SCREAMING_SNAKE_CASE				)[:3]				)				):
      return False
  return True
def 					a__			(				SCREAMING_SNAKE_CASE    :    int = 1_1				):


  '''simple docstring'''







  lowerCAmelCase     :     list[int]								=							[]
  lowerCAmelCase     :     Optional[Any]								=							1_3
  while len(SCREAMING_SNAKE_CASE				) != count:
    if validate(SCREAMING_SNAKE_CASE				):
      lowerCAmelCase     :     int								=							list_truncated_nums(SCREAMING_SNAKE_CASE				)
      if all(is_prime(SCREAMING_SNAKE_CASE				) for i in list_nums				):
        list_truncated_primes.append(SCREAMING_SNAKE_CASE				)
    num += 2
  return list_truncated_primes
def 					a__			(				):


  '''simple docstring'''







  return sum(compute_truncated_primes(1_1				)				)


if __name__ == "__main__":
     print(F"{sum(compute_truncated_primes(11)) = }")









"""simple docstring"""







from __future__ import annotations

from functools import lru_cache
from math import ceil

lowerCAmelCase__      				=   100

lowerCAmelCase__      				=   set(range(3, NUM_PRIMES, 2))
primes.add(2)
lowerCAmelCase__      				=   42

for prime in range(3, ceil(NUM_PRIMES**0.5), 2):
     if prime not in primes:
          continue
     primes.difference_update(set(range(prime * prime, NUM_PRIMES, prime)))
@lru_cache(maxsize=1_0_0				)
def 					a__			(				SCREAMING_SNAKE_CASE    :    int				):


  '''simple docstring'''







  if number_to_partition < 0:
    return set()
  elif number_to_partition == 0:
    return {1}

  lowerCAmelCase     :     set[int]								=							set()
  lowerCAmelCase     :     int
  lowerCAmelCase     :     int

  for prime in primes:
    if prime > number_to_partition:
      continue
    for sub in partition(number_to_partition - prime				):
      ret.add(sub * prime				)

  return ret
def 					a__			(				SCREAMING_SNAKE_CASE    :    int = 5_0_0_0				):


  '''simple docstring'''







  for number_to_partition in range(1				,      SCREAMING_SNAKE_CASE				):
    if len(partition(SCREAMING_SNAKE_CASE				)				) > number_unique_partitions:
      return number_to_partition
  return None


if __name__ == "__main__":
     print(F"{solution() = }")





