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I know that there is a 1965 volume containing the Euler/Goldbach correspondence, but I'm interested in looking at the original manuscripts. I'm not finding anything at University of Basel or Berlin-Brandenburg Academy of Sciences. Any help would be appreciated!

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Leonhardi Euleri Opera omnia: Descriptio commercii epistolici, Volume 1 gives detailed information where the original letters are, or at least were when the book was written) (I take it from your question you know of some partial printed/edited versions available at the link mentioned in a comment). Most of them are in Russia (more specifically to a large extent in the archive of the academy of science of St. Petersburg and another archive in Moscow, something like 'central state archive for old documents'; the book is not in English and I do not know the official names so this is my translation/description of the name; exact names might also have changed as that book was written when the USSR existed).

I do not know whether some scans are online. However it seems that the publication of the respective volume of the Opera Omnia containing the full correspondance is imminent or already happened (I found a page where it said sheduled for 2011).

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  • $\begingroup$ The publication of the Euler-Goldbach correspondence in the Opera Omnia is now scheduled for 2013. $\endgroup$ Commented Feb 10, 2012 at 17:21
  • $\begingroup$ ... and happened in 2015 (Vol. 1, Vol. 2). $\endgroup$ Commented Nov 11, 2019 at 5:42
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The Euler-Goldbach correspondence has been included in the Euler Archive, part of the MAA digital library, at:

http://eulerarchive.maa.org/correspondence/correspondents/Goldbach.html

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  • $\begingroup$ and this improves on Leandro's comment because ... ? $\endgroup$ Commented Oct 24, 2012 at 6:14

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