"""simple docstring"""
def 						__a   (	_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )	->int:
  while b:
    a__							,    a__:     List[str]										=	b, a % b
  return a







def 						__a   (	_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )	->int:
  return a if b == 0 else euclidean_gcd_recursive(_SCREAMING_SNAKE_CASE		,     a % b   )







def 						__a   (	)	->Union[str, Any]:
  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()



"""simple docstring"""
import math







def 						__a   (	_SCREAMING_SNAKE_CASE   )	->bool:

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







def 						__a   (	_SCREAMING_SNAKE_CASE = 0.1   )	->int:
  a__:     str										=	3
  a__:     Optional[Any]										=	3

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


if __name__ == "__main__":
 import doctest

 doctest.testmod()


