He said Tuesday's stage of 138km (86 miles) from Courchevel to Alpe d'Huez, was "absolutely brutal".
For now the three hobnob in Courchevel with other billionaires and share the decisions about where to take the company.
In 2007, Prokhorov was arrested on suspicion of trafficking prostitutes (and released without charge) in the French ski town of Courchevel.
CNN: Prokhorov: Metals mogul hoping to shine in Kremlin race
Every Christmas the three men gather in Courchevel to trade barbs, ski and, most importantly, tend to a Swiss-incorporated metals and mining conglomerate, Eurasian Natural Resources Corp.
Most of the conversation at Courchevel this year was spent figuring out how best to tell their story to smooth the way for a listing on the London Stock Exchange.
Beckham spent the week with his family on holiday at the French skiing resort of Courchevel, but he returned to action on Sunday in Real Madrid's 3-0 home defeat by Osasuna.
After a day carving the slopes in the French Alps, three middle-aged men settle in for tea in the lounge of Les Airelles, a luxurious inn at the top of the mountains in Courchevel, France.
Lance fans who made it to the finish line at the top of the alpine ski resort of Courchevel went wild as their hero took back the leading rider's yellow jersey in a ceremony just after the race.
Despite a tough stage to Courchevel, in which the peloton will tackle the Cornet de Roselend climb that ended Miguel Indurain's reign in 1996, the Alps stages look less gruelling with two valley finishes, in Briancon and Digne.
BBC: SPORT | Other Sport | Cycling | Tour bosses announce 2005 route
The resort has made an effort in recent years to pattern itself after European ski resorts, and added two eateries, Bon Vivant and Alpino Vino, both with decks for sunny weather, which mirror the sort of lunch you might have in Gstaad or Courchevel, a two hour affair over white tablecloths with fine wines and a certain ambiance rarely found in the States.
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