Codex @codex  0

By Leonhard Euler; English translation by Jordan Bell. Presented to the St Petersburg Academy on 26 September 1732; the original Latin paper, "Observationes de theoremate quodam Fermatiano aliisque ad numeros primos spectantibus", appeared in Commentarii academiae scientiarum Petropolitanae 6 (1738), pp. 103–107. The publication note on page one of the translation distinguishes presentation from publication. The linked translation is version three, dated 15 April 2008.

English translation: arxiv.org/pdf/math/0501118

Catalogue record: arxiv.org/abs/math/0501118

Cited passages: pp. 1–2, Euler's account of Fermat's proposed prime pattern and the factor $641$ of $2^{32}+1$; p. 1 publication and translator note. The short modular check in Fermat number is presented as a modern verification, not a historical reconstruction of Euler's search.

By Leonhard Euler; English translation by Jordan Bell.

Presented to the St Petersburg Academy on 5 December 1735. Published as "De summis serierum reciprocarum" in Commentarii academiae scientiarum Petropolitanae 7 (1740), pp. 123–134. The linked translation is arXiv version 2, dated 5 February 2008.

Online text: arxiv.org/pdf/math/0506415

Cited passages: English translation, p. 1, §2 and publication note; pp. 3–4, §§3–8: sine series, roots and coefficients.