The Ternary Goldbach Problem with a prime and two isolated primes (joint paper with M.T. Rassias)

The concept of an isolated prime is closely related to the problem of large gaps between consecutive primes. This problem has mainly been studied by the Erdös - Rankin method and its extensions. Recently a significant improvement of the result has been achieved by Ford, Green, Konyagin, Maynard and Tao. The authors of the present paper combine the results and methods of these five authors with the circle method, which first has been applied to the ternary Goldbach problem by I.M. Vinogradov. His result has been extended to various special sets of primes, e.g. primes in arithmetic progressions. By considering primes in residue-classes, they have constructed by the improved Erdös-Rankin method, the authors obtain the following
Theorem. Under assumption of the Generalized Riemann Hypothesis each sufficiently large odd integer can be expressed as the sum of a prime and two isolated primes.