  n 1937 Ivan Vinogradov proved the three prime sum version of the Goldbach
Conjecture, often called the weak form of Goldbach Conjecture. And that it
holds for "sufficiently large" odd natural numbers. In this work we use
Dirichlet Theorem, Modulo Arithmetics, etc. to extended Vinogradov's Theorem
such that every sufficiently large natural number (both even and odd) can be
expressed as a sum of three primes. We highlight the configuration of primes
for any special case of the three prime sum. Hence we obtain Vinogradov's
Theorem as a special case of this extended version. We show how Vinogradov's
Theorem implies the Goldbach Conjecture; how it (Vinogradov's Theorem) can be
derived from it and vice versa. We also obtain the lower bound of the
sufficiently largeness. And concluding, we highlight some relationships between
the partition function of the Vinogradov's integer w(v) and the Goldbach
integer w(m).
