To the solution of additive problems with prime numbers (Q2857912)

The paper gives a short review of results connected to the Goldbach's problem on the representation of natural numbers as the sum of three primes and some additive problems with prime numbers. The paper only announces some results. Namely, any odd number \(N>N_1=\exp{(\exp{13.465)}}\) is a sum of three primes and any sufficiently large number \(N\) may be represented in the form \(p_1+p_2-p_3\) with \(p_1\), \(p_2\) and \(p_3\) primes and in the form \(p_1-p_2-p_3\). The author announces that the proof is based on the circle method by Hardy-Littlewood-Ramanujan and on the method of trigonometrical sums by Vinogradov.