E228  De numeris, qui sunt aggregata duorum quadratorum
(On numbers which are the sum of two squares)
Summary:
Euler does some examples determining whether certain numbers, like 100981 and 1000009 are prime (yes, and no respectively). Primality testing seems to be his big application here.
According
to C. G. J. Jacobi, a treatise with this title was read to the Berlin Academy on March 20, 1749.
Publication:

Originally published in Novi Commentarii academiae scientiarum Petropolitanae 4, 1758, pp. 340

Opera Omnia: Series 1, Volume 2, pp. 295  327
 Reprinted in Commentat. arithm. 1, 1849, pp. 155173 [E228b]
 A handwritten French translation of this treatise can be found in the library of the observatory in
Uccle, near Brussels.
Documents Available:
 Original publication: E228
 English translation (Paul Bialek): E228
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