

'''simple docstring'''



from numpy import exp, pi, sqrt
def 						__lowerCamelCase	(       __snake_case					:		Dict,		__snake_case					:		float = 0.0,		__snake_case					:		float = 1.0	)	->							List[Any]:






						"""simple docstring"""





						return 1 / sqrt(2 * pi * sigma**2	) * exp(-((x - mu) ** 2) / (2 * sigma**2)	)


if __name__ == "__main__":
						import doctest

						doctest.testmod()




'''simple docstring'''



def 						__lowerCamelCase	(       __snake_case					:		int	)	->							bool:






						"""simple docstring"""





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

						A__					:       Any     =4
						A__					:       int     =(1 << p) - 1
						for _ in range(p - 2	):
												A__					:       Dict     =((s * s) - 2) % m
						return s == 0


if __name__ == "__main__":
		print(lucas_lehmer_test(7))
		print(lucas_lehmer_test(11))

