At the southern end of Central Park, with views towards the mansions of the Upper East Side, 111 West 57th Street is one of the tallest and skinniest skyscrapers on New York City’s so-called Billionaires’ Row. Last year a penthouse in the 82-storey building, known as Steinway Tower, was sold for $52 million (about £41 million), a high price even for a city accustomed to big deals.

That prime price could be knocked out of the park, however, if last week’s reports of a $115 million deal for a duplex penthouse in neighbouring Central Park Tower are true — on a clear day you can just about see the curvature of the Earth from the giddy heights of the seven-bedroom, 12,000 sq ft duplex.