Applied Physics and Mathematics Annotation << Back The distribution of prime tuples in the natural numbers V.L. Vol'fson The work consists of seven of our assertions. At 1-3 the author claims it is proved that the number of prime twins in a natural series of numbers in the more general case of finding and proof of the asymptotic distribution law noncomposite tuples consisting of k primes and prove their infinity in a natural series of numbers. In assertions 4-6 shows that estimates of the number of tuples in a simple non-composite natural numbers, and through a series of improper integral differ by a constant amount. The estimation of this constant from the top. It is shown that in a finite interval estimates of the number of tuples of k prime by a finite sum and the definite integral differ by no more than one tuple, so the two estimates can be used in the practice of computing. 7 In approving an estimate of the number of tuples in a simple constituent of natural numbers. Key words: prime, reduced residue system, module, prime k-tuples, first Hardy–Littlewood conjecture, twin prime, asymptotic distribution, the average density, the asymptotic density, the number, spacing. Contacts: E-mail: znakvicvolf@mail.ru Pp. 64-71.