E461  Extrait d'une lettre de M. Euler le Pere à M. Bernoulli, concernant le Mémoire imprimé parmi ceux de 1771
(Extract of a letter from the elder Mr. Euler to Mr. Bernoulli, concerning the Memoire published among those of 1771)
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 Academieschriften pages at the BerlinBrandenburg Academy of Science's web site, which includes the serial publications of the Prussian Academy of Science from the 18th and 19th Centuries.
 English translation (Todd Doucet): 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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