Pairs with a Great Divisor

Number Theory Level 5

What is the minimum value of \(N\) that will make this statement true:

If we pick any \(N\) composite numbers from 1 to 1000, then we can find 2 numbers whose greatest common divisor is not 1.

Details and assumptions

You may use the fact that there are 168 primes from 1 to 1000.


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