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I am trying to find lower and upper bounds in for the maximum number of integers that are relatively primes per pairs(each other) coprime in pairs 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 a set with at least $π(n)$ integers that are relatively primes prime to each other? where Here $π(n)$ is the number of primes less or equal to $n$.

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Lower bound of the number of relatively primes primes(each-other) in an interval

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 natural numbers of length n.

What are the best bounds that we have?

Is that true that in any interval of natural numbers of length $n$ there are 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 $n$.

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