Fillings Method in Number Theory

In offered work the series of problems of an analytical number theory is surveyed. This problems have direct and defining reflection in prime numbers distribution. For their solving the new method called as a method of fillings was developed. In basis of its the functional imaging lays of the integrated characteristics and elements of all period of generators grids on an interval, and the systems of generators appear as the main object of a research. A fillings method separates from a traditional sieving process already on an initial stage because of this fact. It is necessary to refer possibility of registration and proof of the important state about distribution of the majorizing characteristics of numerical grids on an axe to one of main advantages of a method of fillings. This state is called by the main theorem. Modifications of a relation of the main theorem which is sequentially improved and magnified also were by that source, from which one the concrete outputs about distribution of prime numbers were obtained. The quite particular versatility of the fillings method has allowed to receive outcomes in address to such different tasks as the evaluation of greatest distance between prime numbers, the Goldbach’s conjecture for even, the increase of the Goldbach’s representations, distribution of twins, asymptotics of distribution of typical configurations primes and some others. Thus there are all basis to guess, that possibilities of a method are not exhausted by considered applications, as the method hold sway over not only primes system.