


'''simple docstring'''
import itertools
import math


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


def     a   (    )						->			Tuple:



					'''simple docstring'''






					UpperCamelCase__     :str							      =				2
					while True:
										if is_prime(__a     ):
															yield num
										num += 1


def     a   (    __a = 10001     )						->			int:



					'''simple docstring'''






					return next(itertools.islice(prime_generator()				,      nth - 1				,      __a     )     )


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



'''simple docstring'''
from __future__ import annotations

from decimal import Decimal
from math import *  # noqa: F403

from sympy import diff


def     a   (    __a				,      __a				,      __a = 10**-10     )						->			float:



					'''simple docstring'''






					UpperCamelCase__     :Tuple							      =				a
					while True:
										UpperCamelCase__     :Dict							      =				Decimal(__a     ) - (
										    Decimal(eval(__a     )     ) / Decimal(eval(str(diff(__a     )     )     )     )  # noqa: S307
										)
										# This number dictates the accuracy of the answer
										if abs(eval(__a     )     ) < precision:  # noqa: S307
															return float(__a     )


# Let's Execute
if __name__ == "__main__":
		# Find root of trigonometric function
		# Find value of pi
		print(F"""The root of sin(x) = 0 is {newton_raphson('sin(x)', 2)}""")
		# Find root of polynomial
		print(F"""The root of x**2 - 5*x + 2 = 0 is {newton_raphson('x**2 - 5*x + 2', 0.4)}""")
		# Find Square Root of 5
		print(F"""The root of log(x) - 1 = 0 is {newton_raphson('log(x) - 1', 2)}""")
		# Exponential Roots
		print(F"""The root of exp(x) - 1 = 0 is {newton_raphson('exp(x) - 1', 0)}""")