631 is the area code for Suffolk County, Long Island. All of Long Island was 516 until it was split between the 2 non-NYC counties on the island sometime in the 80's or 90's. A while ago. Nassau County is now 516 by itself.
Of course, there may be some 'grandfathered' numbers involved and other nuances to these specific facts, but as a rule of thumb, 631 is Suffolk.
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