TITLE: Translation of Goldbach's 1742 letter to Euler
QUESTION [17 upvotes]: This ought to be a simple one to answer. Does anyone know of, or can anyone provide, an accurate English translation of the marginal remarks in Goldbach's letter to Euler
http://upload.wikimedia.org/wikipedia/commons/1/18/Letter_Goldbaxh-Euler.jpg
in which a statement equivalent to the Goldbach conjecture is first stated?

REPLY [14 votes]: I have an English translation of the letter; you can find my email address on my homepage. 
Here is the relevant part:
"By the way, I take it to be not useless to note down also such propositions
that are very probable, even if a real proof is lacking; for even if
afterwards they were found to be erroneous, they could all the same give
occasion for the discovery of a new truth. Thus Fermat's idea that all the
numbers $2^{2^{n-1}}+1$ yield a series of prime numbers cannot hold up, as
you already demonstrated, Sir; but it should still be remarkable if this
series were composed only of numbers that could be split into two squares in
a unique way.  I should like to risk another conjecture of that kind: any number 
composed from two primes is the sum of as many prime numbers (including $1$) as one wishes, right down to the sum that consists just of ones.
After reading this through again, I see that the conjecture can be proved 
quite rigorously for the case $n+1$ if it holds for the case $n$ and 
$n+1$ can be split into two prime numbers. The proof is very easy;
and at least it appears to be true that every number greater than 
$2$ is the sum of three prime numbers."
The translation was done by Martin Mattmüller.

REPLY [2 votes]: I do not have the reputation to comment on the answer, so I have to start a new one.
Freely translating page 127 of http://www.math.dartmouth.edu/~euler/correspondence/letters/OO0765.pdf :

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...