
_lowerCamelCase					   =8.3144598





def     _a					(						lowerCamelCase,	lowerCamelCase							):
 if temperature < 0:
  raise Exception("""Temperature cannot be less than 0 K"""							)
 if molar_mass <= 0:
  raise Exception("""Molar mass cannot be less than or equal to 0 kg/mol"""							)
 else:
  return (3 * UNIVERSAL_GAS_CONSTANT * temperature / molar_mass) ** 0.5


if __name__ == "__main__":
      import doctest

      # run doctest
      doctest.testmod()

      # example
      _lowerCamelCase					   =3_0_0
      _lowerCamelCase					   =2_8
      _lowerCamelCase					   =rms_speed_of_molecule(temperature, molar_mass)
      print(f'''Vrms of Nitrogen gas at 300 K is {vrms} m/s''')






def     _a					(						lowerCamelCase							):

 if p < 2:
  raise ValueError("""p should not be less than 2!"""							)
 elif p == 2:
  return True

 lowerCamelCase		:	Any							=      4
 lowerCamelCase		:	List[str]							=      (1 << p) - 1
 for _ in range(p - 2							):
  lowerCamelCase		:	List[Any]							=      ((s * s) - 2) % m
 return s == 0


if __name__ == "__main__":
      print(lucas_lehmer_test(7))
      print(lucas_lehmer_test(1_1))




