





'''simple docstring'''

import math





def 						UpperCamelCase    (							_lowerCamelCase : Optional[Any]	):


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





def 						UpperCamelCase    (							_lowerCamelCase : Optional[int] = 1_00_01	):


				try:
								A__    =      int(_lowerCamelCase	)
				except (TypeError, ValueError):
								raise TypeError("Parameter nth must be int or castable to int."	) from None
				if nth <= 0:
								raise ValueError("Parameter nth must be greater than or equal to one."	)
				A__    =      []
				A__    =      2
				while len(_lowerCamelCase	) < nth:
								if is_prime(_lowerCamelCase	):
												primes.append(_lowerCamelCase	)
												num += 1
								else:
												num += 1
				return primes[len(_lowerCamelCase	) - 1]


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










'''simple docstring'''

def 						UpperCamelCase    (							_lowerCamelCase : int = 1_00_00_00	):
    A__    =      set(range(3						,	_lowerCamelCase						,	2	)	)
    primes.add(2	)
    for p in range(3						,	_lowerCamelCase						,	2	):
        if p not in primes:
            continue
        primes.difference_update(set(range(p * p						,	_lowerCamelCase						,	_lowerCamelCase	)	)	)

    A__    =      [float(_lowerCamelCase	) for n in range(limit + 1	)]

    for p in primes:
        for n in range(_lowerCamelCase						,	limit + 1						,	_lowerCamelCase	):
            phi[n] *= 1 - 1 / p

    return int(sum(phi[2:]	)	)


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



