
"""simple docstring"""




from __future__ import annotations

import math


def   __magic_name__	(      __snake_case				:       int  ) ->				List[str]:

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


_A			:       Optional[Any]   		=       [num for num in range(3, 10_00_01, 2) if not is_prime(num)]


def   __magic_name__	(      __snake_case				:       int  ) ->				int:

       if not isinstance(__a     , __a  ):
              raise ValueError("n must be an integer"  )
       if n <= 0:
              raise ValueError("n must be >= 0"  )

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

       return []


def   __magic_name__	(      ) ->				List[str]:
       return compute_nums(1  )[0]


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




'''simple docstring'''







import os

from huggingface_hub.constants import HUGGINGFACE_HUB_CACHE, hf_cache_home


__lowerCAmelCase         =    HUGGINGFACE_HUB_CACHE


__lowerCAmelCase         =    """config.json"""
__lowerCAmelCase         =    """diffusion_pytorch_model.bin"""
__lowerCAmelCase         =    """diffusion_flax_model.msgpack"""
__lowerCAmelCase         =    """model.onnx"""
__lowerCAmelCase         =    """diffusion_pytorch_model.safetensors"""
__lowerCAmelCase         =    """weights.pb"""
__lowerCAmelCase         =    """https://huggingface.co"""
__lowerCAmelCase         =    default_cache_path
__lowerCAmelCase         =    """diffusers_modules"""
__lowerCAmelCase         =    os.getenv("""HF_MODULES_CACHE""", os.path.join(hf_cache_home, """modules"""))
__lowerCAmelCase         =    ["""fp16""", """non-ema"""]
__lowerCAmelCase         =    """.self_attn"""



