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)
This is a very short note about properties of the numbers 10p, along with criteria for
them to be divisible by 2p+1. It also contains a remark that 231-1 is prime and that
41 - x + xx produces prime numbers for x up to 40.
Originally published in Nouveaux Mémoires de l'Académie des
Sciences de Berlin, Histoire 1772, 1774, pp. 35-36
Opera Omnia: Series 1, Volume 3, pp. 335 - 337
- Reprinted in Commentat. arithm. 1, 1849, pp. 584 [E461a]
- Original publication: E461
- Additionally, E461
can be viewed or downloaded from Academieschriften pages at the Berlin-Brandenburg 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, "Prime-Producing Quadratics," American Mathematical Monthly, 104 (June-July 1997), pp. 529-544.
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