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(TMZ) - Fat Joe has just turned himself in to prison to serve his 4 month sentence for tax evasion, reports TMZ.

The rapper - real name Joseph Cartagena - is officially in custody at the Federal Detention Center in Miami.

As TMZ previously reported, Joe pled guilty back in December to stiffing Uncle Sam on a boatload of taxes for the years 2007 and 2008 ... more than $1 million total.

He originally faced up to two years in the slammer for the crime - but was ultimately sentenced to just 4 months and a $15,000 fine, plus one-year supervised release.

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