

"""simple docstring"""




import itertools
import math
def 	lowerCAmelCase    (       __UpperCamelCase   ):
 '''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 	lowerCAmelCase    (       ):
 '''simple docstring'''





 UpperCAmelCase__       :	Dict        =       2
 while True:
  if is_prime(__UpperCamelCase   ):
   yield num
  num += 1
def 	lowerCAmelCase    (       __UpperCamelCase = 10001   ):
 '''simple docstring'''





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


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







"""simple docstring"""




def     __magic_name__		(					UpperCamelCase     :		float							,		UpperCamelCase     :		float							,		UpperCamelCase     :		float							,		UpperCamelCase     :		float							,		UpperCamelCase     :		float							,		)     ->						float:
    a__		=			[redshift, radiation_density, matter_density, dark_energy]
    if any(p < 0 for p in parameters     ):
        raise ValueError('All input parameters must be positive'     )

    if any(p > 1 for p in parameters[1:4]     ):
        raise ValueError('Relative densities cannot be greater than one'     )
    else:
        a__		=			1 - (matter_density + radiation_density + dark_energy)

        a__		=			(
            radiation_density * (redshift + 1) ** 4
            + matter_density * (redshift + 1) ** 3
            + curvature * (redshift + 1) ** 2
            + dark_energy
        )

        a__		=			hubble_constant * e_a ** (1 / 2)
        return hubble


if __name__ == "__main__":
    import doctest

    # run doctest
    doctest.testmod()

    # demo LCDM approximation
    a		:       Any     						=       0.3

    print(
        hubble_parameter(
            hubble_constant=68.3,
            radiation_density=1e-4,
            matter_density=matter_density,
            dark_energy=1 - matter_density,
            redshift=0,
        )
    )


