



import math


def 			UpperCamelCase(  __UpperCamelCase							:		int ):

		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 			UpperCamelCase(  __UpperCamelCase							:		float = 0.1 ):
		lowerCAmelCase_			:     Optional[Any]									= 3
		lowerCAmelCase_			:     List[str]									= 3

		while primes / (2 * j - 1) >= ratio:
				for i in range(j * j + j + 1     ,(j + 2) * (j + 2)     ,j + 1 ):
						primes += is_prime(__UpperCamelCase )
				j += 2
		return j


if __name__ == "__main__":
						import doctest

						doctest.testmod()






"""simple docstring"""






def   a_						(					lowerCamelCase					,			lowerCamelCase       ):
				if a < 0 or b < 0:
								raise ValueError('the value of both inputs must be positive'       )

				UpperCAmelCase__             =							str(bin(lowerCamelCase       )       )[2:]  # remove the leading "0b"
				UpperCAmelCase__             =							str(bin(lowerCamelCase       )       )[2:]  # remove the leading "0b"

				UpperCAmelCase__             =							max(len(lowerCamelCase       )					,			len(lowerCamelCase       )       )

				return "0b" + "".join(
				    str(int(char_a == '1' and char_b == '1'       )       )
				    for char_a, char_b in zip(a_binary.zfill(lowerCamelCase       )					,			b_binary.zfill(lowerCamelCase       )       )       )


if __name__ == "__main__":
						import doctest

						doctest.testmod()



