Nearly 6,000 serious sex offenders live in NYC — where a legal loophole allows convicted predators to live frighteningly close to schools and children’s playgrounds, The Post has learned.

Paul Brown , a level 3 sex offender — the most serious classification, where the ex-con is considered most likely to re-offend — did seven years in prison for attempting to rape a 7-year-old girl in Brownsville, Brooklyn, according to records and police sources.

Brown was released in November 2009 and returned to custody two more times in 2009 and 2012 for unknown violations, records show.

But because of a loophole in the state law — which prohibits sexual predators from living within 1,000 feet of playgrounds and schools, but only while the offender is on parole or probation — the 49-year-old lives j

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