All gemstones are rare; some are just harder to find than others.
In fact, there is no consensus on what is the rarest mineral or the rarest gemstone because there is no consensus on the definition of "rarity," according to the Gemological Institute of America.
However, many of the stones in this series come from only one or two localities in the entire world, so in that sense, they are scarce.
Pink Star Diamond
In the image above, model Annabeth Murphy-Thomas poses with the Pink Star diamond at Sotheby's auction house in central London. The diamond was put up for auction in Geneva on Nov. 13, 2013, at $60 million, an already record price for a gemstone, and sold for $83 million. Diamond cutter Isaac Wolf of New York purchased the Pink Star diamond ring, and renamed it the Pink Dream. The diamond measures 1.06 inches by 0.81 inches (2.69cm by 2.06cm).