/sci/ - Science & Math » Thread #13107902

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If you pick 2 positive integers at random, the odds of them having no common divisor are...

Anonymous Mon 10 May 06:33:54 2021 No.13107902 View Reply Original Report

Quoted By: >>13109997 >>13113588

6/?2 ? 61%

Well, /sci/?

Anonymous

Anonymous Mon 10 May 2021 15:04:04 No.13109635 Report

Quoted By: >>13109997

You can't "pick a positive integer at random," since each integer would have probability 0 of being picked.

What you mean is that if you pick two integers uniformly from the range 1, 2, ..., N, then the probability that they are relatively prime approachs 6/?^2 as N approaches infinity.

But yeah, other than that, the math checks out.

Anonymous

Anonymous Mon 10 May 2021 16:39:24 No.13109997 Report

Quoted By:

>>13109635
>>13107902
Pretty cool desu, especially given that the reciprocal of that value is the solution to the "Basel problem", but you guys are probably aware, since that is like into real analysis stuff
https://en.wikipedia.org/wiki/Basel_problem

Anonymous

Anonymous Tue 11 May 2021 08:23:09 No.13113453 Report

Quoted By:

If you like probabilistic number theory, then you might like this: https://en.m.wikipedia.org/wiki/Erd?s–Kac_theorem

Anonymous

Anonymous Tue 11 May 2021 09:08:44 No.13113588 Report

Quoted By: >>13114769

>>13107902
>If you pick 2 positive integers at random
How?

Anonymous

Anonymous Tue 11 May 2021 15:50:16 No.13114769 Report

Quoted By:

>>13113588
You flip a coin.
If it's heads then you take 1 and if it's tails you go to the next number and flip the coin again.
If it's heads this time then you take 2 and if it's another tails you go to the next number again and so on.

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