User bertram arnold - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T19:39:34Z http://mathoverflow.net/feeds/user/820 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/23349/translation-of-goldbachs-1742-letter-to-euler/23363#23363 Answer by Bertram Arnold for Translation of Goldbach's 1742 letter to Euler Bertram Arnold 2010-05-03T19:13:46Z 2010-05-03T19:28:04Z <p>I do not have the reputation to comment on the answer, so I have to start a new one.</p> <p>Freely translating page 127 of <a href="http://www.math.dartmouth.edu/~euler/correspondence/letters/OO0765.pdf" rel="nofollow">http://www.math.dartmouth.edu/~euler/correspondence/letters/OO0765.pdf</a> :</p> <blockquote> <p>I deem it to be advantageous to note the following conjecture, even though it lacks a proof, as a counterexample could provide further insights. Fermat's idea that every number of the form \$2^{2^{n-1}}+1\$ is prime can, as you have shown, not be true; but it would be strange if this series yielded a lot of "numeros unico modo in in duo quadratis divisibiles" (numbers that can be divided into two squares???). I, too, would like to hazard a conjecture: that every number that is the sum of two primes is the sum of arbitrary numbers of primes (or 1), except the "congierem omnium unitatum" (the collections of all in one???; the footnote was already translated by Mark), for example...</p> </blockquote>