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A question at math.SE is asking for references. The fraction is quite nice! Check it out and post some references if you know of any.

I found this at arxiv, but it doesn't apply to Zeta.

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  • $\begingroup$ google riemann zeta continued fraction: a paper by S.Apodaca, another one by CVIJOVIC AND KLINOWSKI, a MO post, a Wolfram demo tool. Above inks perhaps not related to MSE question but there are more google results. $\endgroup$
    – Mirko
    Commented Apr 11, 2014 at 17:22
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    $\begingroup$ @user48481MirkoSwirko, thanks for the suggestions. I spent a few hours and didn't find any continued fractions that used only prime numbers. It's looking like Neves's fraction is unique. $\endgroup$
    – Fred Daniel Kline
    Commented Apr 11, 2014 at 19:15
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    $\begingroup$ @Fred Kline, I found that H. J. Brothers is submiting an article with the tittle "The Euler zeta function, continued fractions, and pi". See here. $\endgroup$
    – A.Neves
    Commented Apr 23, 2014 at 9:12
  • $\begingroup$ @A.Neves, Looks like we have to wait to learn more. No preprint on arXiv. Make your comment an answer an I'll sign off with bounty. $\endgroup$
    – Fred Daniel Kline
    Commented Apr 23, 2014 at 9:55

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I found that H. J. Brothers is submiting an article with the tittle "The Euler zeta function, continued fractions, and pi" see here.

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