Was Vinogradov's first proof of the three-prime theorem effective?
Reasons for my question: Vinogradov presented his proof in 1937 in a monograph; the English translation by K.F. Roth and A. Davenport is based on the second version of the monograph, from 1947. There is no doubt that the proof in the second version is effective – Vinogradov goes to great pains to prove a "nearly-log-free" result (as opposed to a bound worse by a factor of $(\log x)^c$, which he proves with much greater ease) because he allows himself to use Siegel-Walfisz only in Page's effective version (= primes are well distributed in arithmetic progressions up to modulus $m\leq (\log n)^{2-\epsilon}$, and exceptions after that in a moderate range would all have to occur for moduli that are multiples of a single modulus of size $> (\log n)^{2-\epsilon}$).
However, I'm finding the 1937 original (in Russian) hard to get. Did he use the usual, ineffective version of Siegel-Walfisz there? Did he already have "nearly-log-free" estimates at the time?
Two more historical questions.
(a) It must have been realized at some point that one does not really need nearly-log-free results to get an effective result (= every odd integer larger than a constant $C$ is the sum of three primes, where $C$ is an enormous constant that can in principle be specified). This is so because there isn't really an exceptional modulus $q$, but, rather, there could be an exceptional character modulo $q$; the other characters modulo $q$ are fine. Thus, Vinogradov's simpler, non-log-free bound is enough for effectivity, even though it's far from optimal. When was this first remarked in the literature? (I can't find any awareness of this in Vinogradov's monograph (translation of 1947 version); he uses Siegel-Walfisz-Page as a black box.)
(b) The first explicit value for $C$ was computed by Borozdkin, who was apparently an assistant and former student of Vinogradov's. The only reference I've got for this is what looks like a mention in the proceedings of a Soviet conference. Did the full version appear anywhere?
Note: I can read Russian, but, like most people working outside Russian-speaking areas, I find many Russian-language historical materials to be hard to get. Links to electronic versions of the documents discussed above would be very welcome.
Best Answer
Concerning question (b). It seems the full version of Borozdkin's proof has never appeared as a normal article. In 1939 he got $C=e^{e^{e^{41.96}}}$ in his unpublished PhD thesis (see http://cheb.tsput.ru/attachments/451_tom13_v2_Kasimov.pdf ). The bound was further improved by him in 1956 to $C=e^{e^{16.038}}$ and a short content of his talk should be in this book (I was not able to find an electronic version) http://www.ozon.ru/context/detail/id/13616734/ on page 3 under the title K voprosu o postoyannoj I. M. Vinogradova.