The flight beat the previous record distance by 540 nautical miles.
The return flight will take an estimated 18 and a half hours, making it the longest commercial flight by duration.
The Trent 500 is the sole powerplant for growth versions of the Airbus A340 and is the latest in-service member of the market-leading Trent family.
The 56,000lb thrust Trent 500 entered service with Virgin Atlantic on August 1, 2002. Since then, 28 aircraft - more than 100 engines - have begun operations with eight customers.
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Click!Rolls-Royce powers 40 out of the world's top 50 airlines and the Trent family is a market leader, having captured 50 per cent of the modern, widebody market.
Throughout 2004, Rolls-Royce plans to celebrate its centenary with a series of special events for customers, partners from education and industry, as well as employees and their families in the UK, Germany, USA and the Far East.