"""simple docstring"""


import math





def       lowerCamelCase_			( __lowerCAmelCase    )							-> bool:




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





def       lowerCamelCase_			( __lowerCAmelCase = 200_0000    )							-> int:




      '''simple docstring'''



      return sum(num for num in range(3       ,   SCREAMING_SNAKE_CASE_       ,   2    ) if is_prime(SCREAMING_SNAKE_CASE_    )    ) + 2 if n > 2 else 0


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



"""simple docstring"""


def       lowerCamelCase_			( __lowerCAmelCase    )							-> bool:




						'''simple docstring'''



						if not isinstance(__lowerCAmelCase       ,   __lowerCAmelCase    ):
												raise ValueError("Input series is not valid, valid series - [2, 4, 8]"    )
						if len(__lowerCAmelCase    ) == 0:
												raise ValueError("Input list must be a non empty list"    )
						if len(__lowerCAmelCase    ) == 1:
												return True
						try:
												lowerCamelCase__ =series[1] / series[0]
												for index in range(len(__lowerCAmelCase    ) - 1    ):
																		if series[index + 1] / series[index] != common_ratio:
																								return False
						except ZeroDivisionError:
												return False
						return True





def       lowerCamelCase_			( __lowerCAmelCase    )							-> float:




						'''simple docstring'''



						if not isinstance(__lowerCAmelCase       ,   __lowerCAmelCase    ):
												raise ValueError("Input series is not valid, valid series - [2, 4, 8]"    )
						if len(__lowerCAmelCase    ) == 0:
												raise ValueError("Input list must be a non empty list"    )
						lowerCamelCase__ =1
						for value in series:
												answer *= value
						return pow(__lowerCAmelCase       ,   1 / len(__lowerCAmelCase    )    )


if __name__ == "__main__":
	import doctest

	doctest.testmod()


