By Philip Elmer-DeWitt
January 22, 2011

It does in 31 months what it took the iTunes Music Store nearly 10 years to achieve

The nines on the app download odometer Apple AAPL posted on its website last week rolled over early Saturday, indicating that 10 billion apps have been downloaded since the store opened for business July 10, 2008.

Somebody — we don’t yet know who — just won a nontransferable $10,000 App Store gift certificate, which if he or she chooses to accept it (and pay taxes on it) could take a lifetime to spend.

[UPDATE: Apple has issued a press release with the name of the winner: “The 10 billionth app downloaded, Paper Glider, was purchased by Gail Davis of Orpington, Kent, UK.”]

Apple says it runs the store slightly above break-even, a claim that’s hard to check because revenue from the App Store is reported in “Other music related products and services,” a line item that includes all iTunes Store sales, iPod services, and Apple-branded and third-party iPod accessories.

But it’s worth noting that even though “Other music-related” grew 88% year over year last quarter, its contribution to Apple’s bottom line was 4% — half of what it was in Q2 and Q3 2009.

Below: The distribution of software categories offered in the store, courtesy of 148Apps.biz.

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[Follow Philip Elmer-DeWitt on Twitter @philiped]

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