#### Name

Bredikhin Boris Andreyevich

#### Scholastic degree

•

#### Academic rank

professor

#### Honorary rank

â€”

#### Organization, job position

Kuban State Agrarian University

#### Web site url

â€”

## Articles count: 3

Problem having elementary formulation makes us
look for its easier solution. So the combinatorial
method of positive integerâ€™s factorization is an
attempt to do it. The combinatory method possesses
simple algorithm, leading immediately to finding out
all the factorizations and identification of all prime
numbers on any interval of the positive integers.
Prime numbers donâ€™t carry any information except
their own magnitude. Composite numbers, possessing
divisibility properties provide possibility to discover
the law of their distribution. The achievement of this
purpose also completely solves the problem of
finding out the law of prime numbersâ€™ distribution

This article is devoted to the assessment of the calculating complexity of combinatory method of numbersâ€™ factorization. The content of combinatory method is explained in the article of the same name published in the journal issued in November 2016. The author supposes that the reader has learnt its content and knows the basic notions of theory of calculating complexity of the algorithms. The following results of the learning of the given task are expounded in this article. The algorithm of combinatory method permits to accomplish the parallel calculations. Graph of any order is the separate structure, because its initial data are determined independently from the other graphs. So, the calculating complexity of the task about the factorization of numbers in the predetermined interval of the positive integers is defined by the complexity of the most laborious graph. The analysis of the graphsâ€™ structure allows to state that itâ€™s the graph of the third order. In any graph both branches of the first level give the separate structures- partitive graphs of the first level with independent input data. So, the calculating complexity of the graph complete is determined by the maximal complexity of the graph of the first level. The givenat random interval of positive integers stays without changes, if we observe the sequence of the adjacent intervals. In the results itâ€™s stated that the assessment of complexity of combinatory method as well other present methods of numbersâ€™factorization is exponential. In this aspect the combinatory method doesnâ€™t compete with other actual methods. However, evaluating the scientific significance of the algorithm, the decisive factor is not the calculating complexity, but its originality, which permits to explain (if not to discover) any properties of the positive integers. In the conclusion of the article the author describes the advantages of combinatory method, permitting to appreciate the degree of its scientific novelty