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.
read more at sloane A130170
MORE ABOUT STAPLED INTERVALS
