(IDEX Online) - Sotheby's New York is to sell an ultra-rare 10.57-carat "bubblegum pink" diamond with an estimate of over $35m.It says the Eternal Pink, a cushion-cut internally flawless fancy vivid purplish pink gem, is the most vivid pink diamond ever to come to market.It also says it could challenge the price per carat record for any diamond or gemstone sold at auction, although that would need a buyer to go way above estimate and pay over $54.7m.Sotheby's says the stone carries the highest price per carat estimate ever placed on any diamond or gemstone ($3,311,258).The record for the price paid per carat actually paid is currently $5,178,124, held by the Williamson Pink Star, a 11.15-carat fancy vivid pink internally flawless diamond.The highest price ever paid for any pink diamond is $71.2m, by China's biggest jeweler, Chow Tai Fook, at an auction held by Sotheby's Hong Kong, in April 2017.The Eternal Pink was was mined by De Beers at the Damtshaa mine, in Botswana, as a 23.78-carat rough stone and was cut by Diacore over a six-month period.It will headline the Sotheby's Magnificent Jewels auction in New York on 8 June after viewings in Hong Kong, Singapore, Shanghai, Taiwan, and Geneva.Pic courtesy Sotheby's.