E461  Extrait d'un lettre de M. Euler le pere a M. Bernoulli concernant le memoire imprime parmi ceux de 1771
(Extract of a letter by Mr. Euler to Mr. Bernoulli father concerning the memoire published by them in 1771, p. 318)
Summary:
This is a very short note about properties of the numbers 10^{p}, along with criteria for
them to be divisible by 2p+1. It also contains a remark that 2^{31}1 is prime and that
41  x + xx produces prime numbers for x up to 40.
Publication:

Originally published in Nouveaux Mémoires de l'Académie des
Sciences de Berlin, Histoire 1772, 1774, pp. 3536

Opera Omnia: Series 1, Volume 3, pp. 335  337
 Reprinted in Commentat. arithm. 1, 1849, pp. 584 [E461a]
Documents Available:
 Original publication: E461
 Additionally, E461
can be viewed or downloaded from Digitalisierte
Akademieschriften und Schriften zur Geschichte der Königlich Preußischen Akademie der
Wissenschaften, which includes serial publications of the Prussian Academy of Science in the 18th and
19th Centuries.
 Ed Sandifer has translated E461
 Other works that cite this paper include:
 R. A. Mollin, "PrimeProducing Quadratics," American Mathematical Monthly, 104 (JuneJuly 1997), pp. 529544.
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