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ON THE REPRESENTATION OF EVEN INTEGERS AS SUM OF TWO ALMOST EQUAL PRIMES

In this paper we generalize the Chudakov van der Corput Estermann Theorem on the exceptional set in the binary Goldbach problem to a result on the same problem with "almost equal" primes. Actually, we prove that the equation Pi +P2 = 2n is satisfied by almost ali 2ra € [N, 2N] when the primes pi and p-2 lie in the interval [n — U, n + U], with U = n^. Furthermore, we explicitly estimate the number of representations of these 2n as sums of such primes.