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Patrick Whitesell Hey Lauren, I Go Prime Too ... Check Out My Hot New GF!!!

Patrick Whitesell's not wasting any time cashing in his most-eligible-bachelor chip -- he's already back in the dating game ... with a stunning Australian model.

Lauren Sanchez's ex-husband stepped out Tuesday night with his incredibly good-looking new girlfriend, Pia Miller. Patrick and the 36-year-old beauty were smiling ear-to-ear, and holding hands as they left WeHo hot spot Craig's.

We broke the story ... Whitesell's divorce with Sanchez -- who's moved on with Amazon honcho Jeff Bezos after he also split from his wife -- is a done deal ... so they're both officially on the market.

It's not much of a surprise they didn't stay available for long -- Lauren's a popular former TV anchor ... and Patrick's co-CEO at William Morris Endeavor worth an estimated $100 million.

Hopefully, they all make the most of another chance at love ... or whatever.

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