Two coprime integers

Two integers are chosen independently and uniformly at random (from a very large range). What is the probability they are coprime (share no common factor > 1)?

Show hints (2)+
  1. Condition on each prime dividing both numbers.
  2. The answer involves ζ(2)=π2/6\zeta(2)=\pi^2/6.

Answer

Reveal answer →

6/π2≈0.60796/\pi^2 \approx 0.6079

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