






from math import isqrt
def 						A__			(				__lowerCAmelCase		:			int						):
						return all(number % divisor != 0 for divisor in range(2   ,    isqrt(_UpperCamelCase						) + 1						)						)
def 						A__			(				__lowerCAmelCase		:			int = 10**6						):
						lowerCamelCase__         =  0
						lowerCamelCase__         =  1
						lowerCamelCase__         =  7
						while prime_candidate < max_prime:
												primes_count += is_prime(_UpperCamelCase						)

												cube_index += 1
												prime_candidate += 6 * cube_index

						return primes_count


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









'''simple docstring'''







import numpy

# List of input, output pairs
UpperCamelCase    :      List[Any]  			=		(
    ((5, 2, 3), 15),
    ((6, 5, 9), 25),
    ((11, 12, 13), 41),
    ((1, 1, 1), 8),
    ((11, 12, 13), 41),
)
UpperCamelCase    :      Optional[int]  			=		(((5_15, 22, 13), 5_55), ((61, 35, 49), 1_50))
UpperCamelCase    :      int  			=		[2, 4, 1, 5]
UpperCamelCase    :      int  			=		len(train_data)
UpperCamelCase    :      Dict  			=		0.009
def 						A__			(				__lowerCAmelCase		:			int   ,    __lowerCAmelCase		:			str="train"						):
						return calculate_hypothesis_value(__lowerCAmelCase   ,    __lowerCAmelCase						) - output(
						    __lowerCAmelCase   ,    __lowerCAmelCase						)
def 						A__			(				__lowerCAmelCase		:			Any						):
						lowerCamelCase__         =  0
						for i in range(len(__lowerCAmelCase						) - 1						):
												hyp_val += data_input_tuple[i] * parameter_vector[i + 1]
						hyp_val += parameter_vector[0]
						return hyp_val
def 						A__			(				__lowerCAmelCase		:			Optional[Any]   ,    __lowerCAmelCase		:			Tuple						):
						if data_set == "train":
												return train_data[example_no][1]
						elif data_set == "test":
												return test_data[example_no][1]
						return None
def 						A__			(				__lowerCAmelCase		:			int   ,    __lowerCAmelCase		:			Dict						):
						if data_set == "train":
												return _hypothesis_value(train_data[example_no][0]						)
						elif data_set == "test":
												return _hypothesis_value(test_data[example_no][0]						)
						return None
def 						A__			(				__lowerCAmelCase		:			List[Any]   ,    __lowerCAmelCase		:			Optional[Any]=m						):
						lowerCamelCase__         =  0
						for i in range(__lowerCAmelCase						):
												if index == -1:
																		summation_value += _error(__lowerCAmelCase						)
												else:
																		summation_value += _error(__lowerCAmelCase						) * train_data[i][0][index]
						return summation_value
def 						A__			(				__lowerCAmelCase		:			List[Any]						):
						lowerCamelCase__         =  summation_of_cost_derivative(__lowerCAmelCase   ,    __lowerCAmelCase						) / m
						return cost_derivative_value
def 						A__			(				):
						global parameter_vector
						# Tune these values to set a tolerance value for predicted output
						lowerCamelCase__         =  0.00_0002
						lowerCamelCase__         =  0
						lowerCamelCase__         =  0
						while True:
												j += 1
												lowerCamelCase__         =  [0, 0, 0, 0]
												for i in range(0   ,    len(__lowerCAmelCase						)						):
																		lowerCamelCase__         =  get_cost_derivative(i - 1						)
																		lowerCamelCase__         =  (
																		    parameter_vector[i] - LEARNING_RATE * cost_derivative
																		)
												if numpy.allclose(
												    __lowerCAmelCase   ,    __lowerCAmelCase   ,    atol=__lowerCAmelCase   ,    rtol=__lowerCAmelCase   ,    ):
																		break
												lowerCamelCase__         =  temp_parameter_vector
						print(("""Number of iterations:""", j)						)
def 						A__			(				):
						for i in range(len(__lowerCAmelCase						)						):
												print(("""Actual output value:""", output(__lowerCAmelCase   ,    """test"""						))						)
												print(("""Hypothesis output:""", calculate_hypothesis_value(__lowerCAmelCase   ,    """test"""						))						)


if __name__ == "__main__":
							run_gradient_descent()
							print('\nTesting gradient descent for a linear hypothesis function.\n')
							test_gradient_descent()

