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Ke Gong kindly sent me a link to Vinogradov's work online:
http://www.mathnet.ru/php/person.phtml?&personid=26537&option_lang=rus
In summary, isit seems clear that the 1937 proof was ineffective.
Questions (a) and (b) remain to be answered.
In summary, is seems clear that the 1937 proof was ineffective.
In summary, it seems clear that the 1937 proof was ineffective.