






from math import isqrt

def      _lowerCamelCase	(						__A    :							str )      ->					list[int]:
    _UpperCAmelCase				:      Optional[int]			  =				[True] * max_number
    for i in range(2		,		isqrt(max_number - 1 ) + 1 ):
        if is_prime[i]:
            for j in range(i**2		,		__A		,		__A ):
                _UpperCAmelCase				:      int			  =				False

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

def      _lowerCamelCase	(						__A    :							Any = 10**8 )      ->					int:
    _UpperCAmelCase				:      List[str]			  =				calculate_prime_numbers(max_number // 2 )

    _UpperCAmelCase				:      Optional[Any]			  =				0
    _UpperCAmelCase				:      Union[str, Any]			  =				0
    _UpperCAmelCase				:      Optional[Any]			  =				len(__A ) - 1
    while left <= right:
        while prime_numbers[left] * prime_numbers[right] >= max_number:
            right -= 1
        semiprimes_count += right - left + 1
        left += 1

    return semiprimes_count


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












import numpy as np
import skfuzzy as fuzz

if __name__ == "__main__":
  # Create universe of discourse in Python using linspace ()
  SCREAMING_SNAKE_CASE 							=						np.linspace(start=0, stop=75, num=75, endpoint=True, retstep=False)

  # Create two fuzzy sets by defining any membership function
  # (trapmf(), gbellmf(), gaussmf(), etc).
  SCREAMING_SNAKE_CASE 							=						[0, 25, 50]
  SCREAMING_SNAKE_CASE 							=						[25, 50, 75]
  SCREAMING_SNAKE_CASE 							=						fuzz.membership.trimf(X, abca)
  SCREAMING_SNAKE_CASE 							=						fuzz.membership.trimf(X, abca)

  # Compute the different operations using inbuilt functions.
  SCREAMING_SNAKE_CASE 							=						np.ones(75)
  SCREAMING_SNAKE_CASE 							=						np.zeros((75,))
  # 1. Union = max(µA(x), µB(x))
  SCREAMING_SNAKE_CASE 							=						fuzz.fuzzy_or(X, young, X, middle_aged)[1]
  # 2. Intersection = min(µA(x), µB(x))
  SCREAMING_SNAKE_CASE 							=						fuzz.fuzzy_and(X, young, X, middle_aged)[1]
  # 3. Complement (A) = (1- min(µA(x))
  SCREAMING_SNAKE_CASE 							=						fuzz.fuzzy_not(young)
  # 4. Difference (A/B) = min(µA(x),(1- µB(x)))
  SCREAMING_SNAKE_CASE 							=						fuzz.fuzzy_and(X, young, X, fuzz.fuzzy_not(middle_aged)[1])[1]
  # 5. Algebraic Sum = [µA(x) + µB(x) – (µA(x) * µB(x))]
  SCREAMING_SNAKE_CASE 							=						young + middle_aged - (young * middle_aged)
  # 6. Algebraic Product = (µA(x) * µB(x))
  SCREAMING_SNAKE_CASE 							=						young * middle_aged
  # 7. Bounded Sum = min[1,(µA(x), µB(x))]
  SCREAMING_SNAKE_CASE 							=						fuzz.fuzzy_and(X, one, X, young + middle_aged)[1]
  # 8. Bounded difference = min[0,(µA(x), µB(x))]
  SCREAMING_SNAKE_CASE 							=						fuzz.fuzzy_or(X, zero, X, young - middle_aged)[1]

  # max-min composition
  # max-product composition

  # Plot each set A, set B and each operation result using plot() and subplot().
  from matplotlib import pyplot as plt

  plt.figure()

  plt.subplot(4, 3, 1)
  plt.plot(X, young)
  plt.title('Young')
  plt.grid(True)

  plt.subplot(4, 3, 2)
  plt.plot(X, middle_aged)
  plt.title('Middle aged')
  plt.grid(True)

  plt.subplot(4, 3, 3)
  plt.plot(X, union)
  plt.title('union')
  plt.grid(True)

  plt.subplot(4, 3, 4)
  plt.plot(X, intersection)
  plt.title('intersection')
  plt.grid(True)

  plt.subplot(4, 3, 5)
  plt.plot(X, complement_a)
  plt.title('complement_a')
  plt.grid(True)

  plt.subplot(4, 3, 6)
  plt.plot(X, difference)
  plt.title('difference a/b')
  plt.grid(True)

  plt.subplot(4, 3, 7)
  plt.plot(X, alg_sum)
  plt.title('alg_sum')
  plt.grid(True)

  plt.subplot(4, 3, 8)
  plt.plot(X, alg_product)
  plt.title('alg_product')
  plt.grid(True)

  plt.subplot(4, 3, 9)
  plt.plot(X, bdd_sum)
  plt.title('bdd_sum')
  plt.grid(True)

  plt.subplot(4, 3, 10)
  plt.plot(X, bdd_difference)
  plt.title('bdd_difference')
  plt.grid(True)

  plt.subplots_adjust(hspace=0.5)
  plt.show()




