I found the answer to a very similar question already asked here on mathoverflow: what is the probability that two natural numbers are relatively prime? The answer given in the link below was $\frac{6}{\pi^2}$.

What is the probability that two numbers are relatively prime?

My question is a little more specific: if two integers are randomly selected from the interval $[a,b]$, what is the probability that they are relatively prime?

I'd guess that as $a$ and $b$ get farther apart, the probability would approach the same $\frac{6}{\pi^2}$. I'm trying to find an answer for when $a$ and $b$ are quite large, say around $2^{128}$, but I'd love to see an analysis for general integers. Since the similar question was already answered above, I wouldn't think it would be much work to solve the problem on a smaller interval.


closed as off-topic by Will Jagy, Franz Lemmermeyer, Jan-Christoph Schlage-Puchta, Stefan Kohl, Christian Remling Jul 10 '16 at 16:49

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  • $\begingroup$ What have you tried, and how large is (b-a)? I don't see the answer being much different from the probability over all natural numbers. Gerhard "Up To Rounding Error, Naturally" Paseman, 2016.07.10. $\endgroup$ – Gerhard Paseman Jul 10 '16 at 15:09