What is the rarest Japanese sword?

Could you please elaborate on what makes a Japanese sword particularly rare? Is it the age, the craftsmanship, or perhaps the historical significance attached to it? When it comes to the rarest Japanese sword, are we looking at a specific type, such as a tachi, katana, or wakizashi? And if so, what sets this particular sword apart from the rest, making it stand out as the rarest of its kind? Is there a specific story or legend surrounding this sword that adds to its rarity and mystique?