
import itertools
import math






def   lowerCamelCase__							(					a      )      ->   Optional[Any]:

   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(snake_case_      ) + 1      )		,		6      ):
      if number % i == 0 or number % (i + 2) == 0:
         return False
   return True






def   lowerCamelCase__							(					)      ->   Union[str, Any]:
   _A:  Dict					=       2
   while True:
      if is_prime(snake_case_      ):
         yield num
      num += 1






def   lowerCamelCase__							(					a = 1_00_01      )      ->   Optional[Any]:
   return next(itertools.islice(prime_generator()		,		nth - 1		,		snake_case_      )      )


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









def 				lowerCAmelCase_	(     snake_case_,snake_case_     ):
      while b:
            _A			,   _A							:     List[str]			=						b, a % b
      return a







def 				lowerCAmelCase_	(     snake_case_,snake_case_     ):
      return a if b == 0 else euclidean_gcd_recursive(snake_case_,a % b     )







def 				lowerCAmelCase_	(     ):
      print(f'''euclidean_gcd(3, 5) = {euclidean_gcd(3,5     )}'''     )
      print(f'''euclidean_gcd(5, 3) = {euclidean_gcd(5,3     )}'''     )
      print(f'''euclidean_gcd(1, 3) = {euclidean_gcd(1,3     )}'''     )
      print(f'''euclidean_gcd(3, 6) = {euclidean_gcd(3,6     )}'''     )
      print(f'''euclidean_gcd(6, 3) = {euclidean_gcd(6,3     )}'''     )

      print(f'''euclidean_gcd_recursive(3, 5) = {euclidean_gcd_recursive(3,5     )}'''     )
      print(f'''euclidean_gcd_recursive(5, 3) = {euclidean_gcd_recursive(5,3     )}'''     )
      print(f'''euclidean_gcd_recursive(1, 3) = {euclidean_gcd_recursive(1,3     )}'''     )
      print(f'''euclidean_gcd_recursive(3, 6) = {euclidean_gcd_recursive(3,6     )}'''     )
      print(f'''euclidean_gcd_recursive(6, 3) = {euclidean_gcd_recursive(6,3     )}'''     )


if __name__ == "__main__":
  main()

