So many couples want to marry July 24, the first day gay couples can legally wed, that the city has created a lottery limiting spots.

Mayor Michael Bloomberg announced today that the City Clerk’s office received 2,661 applications since July 5.

About half of the applicants wanted to visit the Clerk’s Office on July 25 and get married that same day.

“It’s clear that the number of couples who want to marry on Sunday is more than the City Clerk’s offices could possibly handle,” Bloomberg said.

To make sure that a slew of couples don’t show up unable to get hitched, the city will have a lottery for 764 couples who can go to the City Clerk’s five offices.

Couples who want to marry need to register for the lottery at the City Clerk’s website or call 311.

Only couples winning the lottery should plan to marry Sunday, a Bloomberg spokesman said. Instead, they should come on a weekday.

The 764 couples to marry Sunday will the most on any single day in the city’s history.

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