




from __future__ import annotations

import math



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


UpperCamelCase								=	[num for num in range(3, 10_0001, 2) if not is_prime(num)]



def 				_A  (		lowerCAmelCase_	:   int     ):
     """simple docstring"""

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

     lowerCAmelCase__            =					[]
     for num in range(len(lowerCAmelCase_     )     ):
          lowerCAmelCase__            =					0
          while 2 * i * i <= odd_composites[num]:
               lowerCAmelCase__            =					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  (		):
     """simple docstring"""

     return compute_nums(1     )[0]


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








"""simple docstring"""
def 				lowercase__		(					lowerCamelCase,						lowerCamelCase       ):
				return numa ^ numa < 0


if __name__ == "__main__":
			import doctest

			doctest.testmod()

