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I am looking for examples of infinite pairwise coprime sets.

A set P of integers is pairwise coprime iff, for every p and q in P with p ≠ q, we have gcd(p, q) = 1. Here gcd denotes the greatest common divisor.(Wikipedia)

Also from wikipedia the following are some examples of infinite such sets:

Theset of all primes, {2, 3, 5, 7, 11, …} is of course pairwise coprime, as is the set of elements inSylvester's sequence, and the set of allFermat numbers(Wikipedia).

However, the set of all primes is trivial and two broad of a set for my purpose, and the last two seem to be too restrective, in the sense that their terms get very big very fast, which is something i would not like to deal with.

So, i guess what i am looking for is something in beetween. Also, i believe that a finite set of integers that is pairwise coprime would work, as long as it is a relatively large set.

Also i am wondering, whether there are pairwise coprime sets of any desired lenght? That is, for any given k in Z, is it possible to find a pairwise coprime set P with exactly k elements in it?

Thanks to all of you!

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# Pairwise coprime sets?

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