


import itertools
import math







def        lowerCAmelCase_  (      __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        lowerCAmelCase_  (      ):
							__snake_case	:    Optional[int]											=     2
							while True:
														if is_prime(__lowerCamelCase			):
																					yield num
														num += 1







def        lowerCAmelCase_  (      __lowerCamelCase = 1_0_0_0_1			):
							return next(itertools.islice(prime_generator()							,			nth - 1							,			__lowerCamelCase			)			)


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





def        lowerCAmelCase_  (      __lowerCamelCase							,			__lowerCamelCase			):
							if number < 0 or shift_amount < 0:
														raise ValueError("both inputs must be positive integers"			)

							__snake_case	:    Dict											=     str(bin(__lowerCamelCase			)			)
							binary_number += "0" * shift_amount
							return binary_number







def        lowerCAmelCase_  (      __lowerCamelCase							,			__lowerCamelCase			):
							if number < 0 or shift_amount < 0:
														raise ValueError("both inputs must be positive integers"			)

							__snake_case	:    List[str]											=     str(bin(__lowerCamelCase			)			)[2:]
							if shift_amount >= len(__lowerCamelCase			):
														return "0b0"
							__snake_case	:    Union[str, Any]											=     binary_number[: len(__lowerCamelCase			) - shift_amount]
							return "0b" + shifted_binary_number







def        lowerCAmelCase_  (      __lowerCamelCase							,			__lowerCamelCase			):
							if number >= 0:  # Get binary representation of positive number
														__snake_case	:    Optional[int]											=     "0" + str(bin(__lowerCamelCase			)			).strip("-"			)[2:]
							else:  # Get binary (2's complement) representation of negative number
														__snake_case	:    Tuple											=     len(bin(__lowerCamelCase			)[3:]			)  # Find 2's complement of number
														__snake_case	:    Any											=     bin(abs(__lowerCamelCase			) - (1 << binary_number_length)			)[3:]
														__snake_case	:    Optional[Any]											=     (
														    "1" + "0" * (binary_number_length - len(__lowerCamelCase			)) + binary_number
														)

							if shift_amount >= len(__lowerCamelCase			):
														return "0b" + binary_number[0] * len(__lowerCamelCase			)
							return (
							    "0b"
							    + binary_number[0] * shift_amount
							    + binary_number[: len(__lowerCamelCase			) - shift_amount]
							)


if __name__ == "__main__":
			import doctest

			doctest.testmod()

