

"""simple docstring"""





import math




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




def     _A    (    UpperCamelCase_	:			int = 2000000)      ->		int:
   '''simple docstring'''


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


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







"""simple docstring"""





def     _A    (    UpperCamelCase_	:			int,     UpperCamelCase_	:			int = 1000)      ->		str:
   '''simple docstring'''


   if (not isinstance(UpperCamelCase_,     UpperCamelCase_)) or (digit_position <= 0):
      raise ValueError("Digit position must be a positive integer")
   elif (not isinstance(UpperCamelCase_,     UpperCamelCase_)) or (precision < 0):
      raise ValueError("Precision must be a nonnegative integer")

   # compute an approximation of (16 ** (n - 1)) * pi whose fractional part is mostly
   # accurate
   __lowercase								=		(
       4 * _subsum(UpperCamelCase_,     1,     UpperCamelCase_)
       - 2 * _subsum(UpperCamelCase_,     4,     UpperCamelCase_)
       - _subsum(UpperCamelCase_,     5,     UpperCamelCase_)
       - _subsum(UpperCamelCase_,     6,     UpperCamelCase_)
   )

   # return the first hex digit of the fractional part of the result
   return hex(int((sum_result % 1) * 16))[2:]




def     _A    (    UpperCamelCase_	:			int,     UpperCamelCase_	:			int,     UpperCamelCase_	:			int)      ->		float:
   '''simple docstring'''


   __lowercase								=		0.0
   for sum_index in range(digit_pos_to_extract + precision):
      __lowercase								=		8 * sum_index + denominator_addend
      if sum_index < digit_pos_to_extract:
         # if the exponential term is an integer and we mod it by the denominator
         # before dividing, only the integer part of the sum will change;
         # the fractional part will not
         __lowercase								=		pow(
             16,     digit_pos_to_extract - 1 - sum_index,     UpperCamelCase_)
      else:
         __lowercase								=		pow(16,     digit_pos_to_extract - 1 - sum_index)
      total += exponential_term / denominator
   return total


if __name__ == "__main__":
   import doctest

   doctest.testmod()




