RAPAPORT... One of the purest pink diamonds in history will go under the hammer at Sotheby's later this year, carrying a presale estimate of HKD 170 million ($21 million).The cushion-cut, 11.15-carat, fancy-vivid-pink, internally flawless stone, named the Williamson Pink Star, will appear at a stand-alone sale in Hong Kong on October 5, Sotheby's said Wednesday. It is the second-largest diamond of that color and clarity ever to feature at auction, behind the 59.60-carat CTF Pink Star, which fetched a record $71.2 million at Sotheby's in 2017."Driven by a limited supply and rising demand, prices for top-quality large pink diamonds over 5 carats have increased exponentially over the past decade," said Wenhao Yu, chairman of jewelry and watches at Sotheby's Asia.At the estimated price, the stone would sell for around $1.9 million per carat. That compares with $1.2 million per carat for the CTF Pink Star.The stone originates from a 32.32-carat rough from Petra Diamonds' Williamson mine in Tanzania. Polished manufacturer Diacore bought the rough for $13.8 million at a tender last year and cut it into the cushion-shaped diamond that's up for sale.The name is a nod to both the CTF Pink Star and the Williamson stone, a brilliant-cut, 23.60-carat diamond that Queen Elizabeth II received as a wedding present in 1947 from Canadian geologist and royalist Dr. John Thorburn Williamson. Williamson owned the mine that bears his name in Mwadui, Tanzania, where that stone was discovered.Image: The Williamson Pink Star. (Sotheby's)