What is the first set of consecutive positive integers such that every number has a common factor greater than 1 with at least one other number in the set?

Very good problem- I rated it 5.

I believe the source is Sloane A090318 A130170 A130173

`An interval is stapled if for every element x there is another element y (different from x) such that gcd(x,y)>1.`

`The shortest stapled interval has length 17 and starts with the number 2184.`

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