He checked it against thousands of cases and always found it to be true - but the whole numbers being infinite, only an abstract proof would cover the general case. This he could not find.
Every odd number is the sum of three primes.
The second GC was proven in the mid 1930's by the great Russian number theorist, Ivan Vinogradov. Because of its notorious difficulty, GC is not the kind of problem that attracts many top class researchers today. Few people want to waste years and years working on a problem that in all probability they will not solve. Mathematics, like all scientific disciplines, is ruled by expediency and fashion, and the classical problems of number theory are not currently deemed la mode . One more reason that a major breakthrough with GC seems unlikely in the foreseeable future The closest anyone has come to proving GC is a theorem of 1996 by the Chinese mathematician Chen Jing-Run.