If a prime is greater than the length of the segment (for example, $30$), there is at most one number in the segment that is divisible by it. So, if a number appears in $15$ or more pairs that are not fixed by primes less than $30$, every such pair should be "fixed" by a separate prime.
If a prime is greater than the length of the segment (for example, $30$), there is at most one number in the segment that is divisible by it. So, if a number appears in $15$ or more pairs that are not fixed by primes less than $30$, every such pair should be "fixed" by a separate prime.