E369 -- Quomodo numeri praemagni sint explorandi, utrum sint primi necne
(How very large numbers are to be tested for whether they are prime or not)
Euler uses representations in the form xx+yy to determine whether or not numbers are prime. He finds factors of several large numbers. He presents several theorems, without proofs, about the forms of x that allow xx+yy to satisfy certain congruences.
to the records, it was presented to the St. Petersburg Academy on December 19, 1765.
Originally published in Novi Commentarii academiae scientiarum Petropolitanae 13, 1769, pp. 67-88
Opera Omnia: Series 1, Volume 3, pp. 112 - 130
- Reprinted in Commentat. arithm. 1, 1849, pp. 379-390 [E369a]
- A handwritten French translation of this treatise can be found in the library of the observatory in
Uccle, near Brussels.
- Original publication: E369
Return to the Euler Archive