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Only three or four blue diamonds over 100 carats have ever been recovered, according to Cathy Mallins, corporate communications manager at Petra Diamonds Ltd.
So far, the highest price on record for a rough diamond is $US35.3 million, paid in February 2010 for a 507-carat white stone recovered from the same mine, finnCap analyst Martin Potts said in a research note.
"We think that this stone may break that record," he said.
Both diamonds were recovered from the Cullinan mine, the source of many large diamonds, including the largest rough gem diamond ever recovered - the 3,106-carat Cullinan Diamond found in 1905.
That diamond was cut into two stones that are part of Britain's Crown Jewels held in the Tower of London.
Petra's shares rose as much as 7 percent on Friday, making them the top percentage gainer on the FTSE-250 Midcap Index .
Petra said it would evaluate the optimal route to market the stone after further analysis to assess its potential value.
Last month, a 100-carat yellow diamond fetched $US16.3 million at a Sotheby's auction in Geneva - the highest amount ever paid for a diamond of that colour. The rough stone was 190 carats.
"Given that blue diamonds are rarer, more desirable than both yellow and white stones, we would expect multiples of this in terms of value," Numis analysts said in a note.
"If it comes back from analysis as 'fancy vivid' colour then it could blow the roof off."
Other notable diamonds discovered at the mine include the 25.5-carat Cullinan blue diamond found in 2013, and sold for $US16.9 million, and the Star of Josephine diamond recovered in 2008, which sold for $US9.49 million.
Petra bought Cullinan in 2008. The mine, located at the foothills of the Magaliesberg mountain range north-east of Pretoria, is one of the company's five producing mines in South Africa. It also has mine in Tanzania.