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(I am assuming you mean New York, NY, USA)
And of course there is no answer in "road miles".
Using Google Earth there is a tool that looks like a little ruler on the tool bar above the display window. You can use it to measure distances such as this. I am assuming that it gives a valid great circle distance when used over this large a distance.
That said, the distance between Gothenburg (Sweden) and New York, NY is:
3,774 miles (or approx. 6,077 km)
What else can I help you with?
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