By Philip Elmer-DeWitt

    Apple (AAPL) announced Tuesday that its customers have downloaded more than 1.5 billion applications in the year since its iPhone App Store — “the largest applications store in the world” — opened for business.

    There was no countdown odometer this time — as there was for the 1 billion mark last April — and no prizes for the user who downloaded the last app.

    Just a press releasefrom Apple PR and a self-congratulatory quote from Cupertino’s prodigal CEO:

    “The App Store is like nothing the industry has ever seen before in both scale and quality,” said Steve Jobs, who couldn’t resist adding a small dig at the competition. “With 1.5 billion apps downloaded, it is going to be very hard for others to catch up.”

    One of the factors feeding the App Store’s growth — and in turn being fed by it — is the size of the installed base: 40 million iPhones and iPod touches according to Tuesday’s release, a number likely to grow when Apple announces its fiscal third quarter earnings next week.

    The other is the variety and sheer quantity of applications to choose from — 65,000 according to Apple’s press release, 58,000 of them in the U.S. App Store, according to 148Apps.biz’s independent count, and another 7,000 in the App Store’s 70-plus overseas branches.

    Logic would suggest that this breakneck growth can’t continue forever. But the rate of downloads took off late last year and, as the slope of the curve below suggests, hasn’t slowed since.