



'''simple docstring'''





from __future__ import annotations

import math

def 			a_	(				_lowerCAmelCase			) -> bool:

  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(_lowerCAmelCase			) + 1			)			,6			):
    if number % i == 0 or number % (i + 2) == 0:
      return False
  return True


_UpperCamelCase											=		[num for num in range(3, 100001, 2) if not is_prime(num)]

def 			a_	(				_lowerCAmelCase			) -> list[int]:
  if not isinstance(_lowerCAmelCase			,_lowerCAmelCase			):
    raise ValueError('n must be an integer'			)
  if n <= 0:
    raise ValueError('n must be >= 0'			)

  __lowerCamelCase			:			Tuple       			=					[]
  for num in range(len(_lowerCAmelCase			)			):
    __lowerCamelCase			:			Optional[Any]       			=					0
    while 2 * i * i <= odd_composites[num]:
      __lowerCamelCase			:			List[Any]       			=					odd_composites[num] - 2 * i * i
      if is_prime(_lowerCAmelCase			):
        break
      i += 1
    else:
      list_nums.append(odd_composites[num]			)
      if len(_lowerCAmelCase			) == n:
        return list_nums

  return []

def 			a_	(				) -> int:
  return compute_nums(1			)[0]


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











'''simple docstring'''





from __future__ import annotations

_UpperCamelCase											=		10

def 			a_	(				_lowerCAmelCase			) -> list[int]:
  __lowerCamelCase			:			str       			=					1
  __lowerCamelCase			:			Union[str, Any]       			=					max(_lowerCAmelCase			)
  while placement <= max_digit:
    # declare and initialize empty buckets
    __lowerCamelCase			:			list[list]       			=					[[] for _ in range(_lowerCAmelCase			)]
    # split list_of_ints between the buckets
    for i in list_of_ints:
      __lowerCamelCase			:			List[str]       			=					int((i / placement) % RADIX			)
      buckets[tmp].append(_lowerCAmelCase			)
    # put each buckets' contents into list_of_ints
    __lowerCamelCase			:			Dict       			=					0
    for b in range(_lowerCAmelCase			):
      for i in buckets[b]:
        __lowerCamelCase			:			List[str]       			=					i
        a += 1
        # move to next
    placement *= RADIX
  return list_of_ints


if __name__ == "__main__":
   import doctest

   doctest.testmod()






