






"""simple docstring"""
import math





def 				lowercase__		(					lowerCamelCase       ):

				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 				lowercase__		(					lowerCamelCase = 0.1       ):
				_SCREAMING_SNAKE_CASE   :		List[str]       		=    3
				_SCREAMING_SNAKE_CASE   :		int       		=    3

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


if __name__ == "__main__":
			import doctest

			doctest.testmod()









"""simple docstring"""
def 				lowercase__		(					lowerCamelCase,						lowerCamelCase       ):
				return numa ^ numa < 0


if __name__ == "__main__":
			import doctest

			doctest.testmod()

