






from ..utils import DummyObject, requires_backends




class       snake_case__ (				metaclass=__snake_case):

       '''simple docstring'''
       lowerCamelCase				:					Any								=			["torch", "torchsde"]



       def __init__(				self      ,    *a__      ,    **a__     )			->   Tuple:






            '''simple docstring'''





            requires_backends(self      ,    ["""torch""", """torchsde"""]     )



       @classmethod
       def        __lowercase    (				cls      ,    *a__      ,    **a__     )			->   str:






            '''simple docstring'''





            requires_backends(cls      ,    ["""torch""", """torchsde"""]     )



       @classmethod
       def        __lowercase    (				cls      ,    *a__      ,    **a__     )			->   Union[str, Any]:






            '''simple docstring'''





            requires_backends(cls      ,    ["""torch""", """torchsde"""]     )






from __future__ import annotations

import math
def 	_UpperCamelCase					(    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


__a	 =      [num for num in range(3, 10_0001, 2) if not is_prime(num)]
def 	_UpperCamelCase					(    lowerCAmelCase_ )    ->list[int]:
   if not isinstance(lowerCAmelCase_	,    lowerCAmelCase_ ):
      raise ValueError("""n must be an integer""" )
   if n <= 0:
      raise ValueError("""n must be >= 0""" )

   UpperCAmelCase      					=  []
   for num in range(len(lowerCAmelCase_ ) ):
      UpperCAmelCase      					=  0
      while 2 * i * i <= odd_composites[num]:
         UpperCAmelCase      					=  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 	_UpperCamelCase					(    )    ->int:
   return compute_nums(1 )[0]


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



