






"""simple docstring"""



from math import isqrt, loga


def 	SCREAMING_SNAKE_CASE__       (  snake_case       : int				)->		list[int]:






     '''simple docstring'''



     UpperCAmelCase__						:    Dict							=							[True] * max_number
     for i in range(2			,					isqrt(max_number - 1				) + 1				):
          if is_prime[i]:
               for j in range(i**2			,					snake_case			,					snake_case				):
                    UpperCAmelCase__						:    Dict							=							False

     return [i for i in range(2			,					snake_case				) if is_prime[i]]


def 	SCREAMING_SNAKE_CASE__       (  snake_case       : int = 80_0800			,					snake_case       : int = 80_0800				)->		int:






     '''simple docstring'''



     UpperCAmelCase__						:    str							=							degree * loga(snake_case				)
     UpperCAmelCase__						:    List[str]							=							int(snake_case				)
     UpperCAmelCase__						:    List[Any]							=							calculate_prime_numbers(snake_case				)

     UpperCAmelCase__						:    Optional[Any]							=							0
     UpperCAmelCase__						:    Tuple							=							0
     UpperCAmelCase__						:    Optional[Any]							=							len(snake_case				) - 1
     while left < right:
          while (
              prime_numbers[right] * loga(prime_numbers[left]				)
              + prime_numbers[left] * loga(prime_numbers[right]				)
              > upper_bound
          ):
               right -= 1
          hybrid_integers_count += right - left
          left += 1

     return hybrid_integers_count


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










"""simple docstring"""



def 	SCREAMING_SNAKE_CASE__       (  snake_case       : int			,					snake_case       : int				)->		str:






     '''simple docstring'''



     if not isinstance(snake_case			,					snake_case				):
          raise ValueError("iterations must be defined as integers"				)
     if not isinstance(snake_case			,					snake_case				) or not number >= 1:
          raise ValueError(
              "starting number must be\n                         and integer and be more than 0"				)
     if not iterations >= 1:
          raise ValueError("Iterations must be done more than 0 times to play FizzBuzz"				)

     UpperCAmelCase__						:    str							=							""
     while number <= iterations:
          if number % 3 == 0:
               out += "Fizz"
          if number % 5 == 0:
               out += "Buzz"
          if 0 not in (number % 3, number % 5):
               out += str(snake_case				)

          # print(out)
          number += 1
          out += " "
     return out


if __name__ == "__main__":
 import doctest

 doctest.testmod()


