I am trying to find lower and upper bounds in the maximum number of integers that are relatively primes per pairs(each other) in an interval of length n. 

>What are the best bounds that we have?

>Is that true that in any interval  of length $n$ there is aset with  at least $π(n)$ integers that are relatively primes each other? where  $π(n)$ is the number of primes less or equal to $n$.