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Glorfindel
Glorfindel
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The probability that two Gaussian integers are relatively prime is $6/(\pi^2 K) = 0.66370080461385348\cdots$, where $K= 1 - \frac{1}{3^2}+\frac{1}{5^2}-\frac{1}{7^2}+\cdots$ (Catalan's constant). There is no known simple expression for $K$ in terms of $\pi$. See http://www.springerlink.com/content/y826m64747254t87Link.

The probability that two Gaussian integers are relatively prime is $6/(\pi^2 K) = 0.66370080461385348\cdots$, where $K= 1 - \frac{1}{3^2}+\frac{1}{5^2}-\frac{1}{7^2}+\cdots$ (Catalan's constant). There is no known simple expression for $K$ in terms of $\pi$. See http://www.springerlink.com/content/y826m64747254t87.

The probability that two Gaussian integers are relatively prime is $6/(\pi^2 K) = 0.66370080461385348\cdots$, where $K= 1 - \frac{1}{3^2}+\frac{1}{5^2}-\frac{1}{7^2}+\cdots$ (Catalan's constant). There is no known simple expression for $K$ in terms of $\pi$. See Link.

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Richard Stanley
Richard Stanley
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The probability that two Gaussian integers are relatively prime is $6/(\pi^2 K) = 0.66370080461385348\cdots$, where $K= 1 - \frac{1}{3^2}+\frac{1}{5^2}-\frac{1}{7^2}+\cdots$ (Catalan's constant). There is no known simple expression for $K$ in terms of $\pi$. See http://www.springerlink.com/content/y826m64747254t87.