Applied Physics and Mathematics Annotation << Back ASYMPTOTIC OF THE GREATEST DISTANCE BETWEEN ADJACENT PRIMES AND THE HARDY-LITTLEWOOD CONJECTURE V.L. VOLFSON Recently, with the development of computer technology and the Internet, the problem of the distribution of primes has acquired important practical importance, since it is directly related to the reliability of the so-called cryptographic systems with a public key. For example, the cryptographic strength of the currently widely used RSA encryption system is based on the computational complexity of factorization of large natural numbers. The paper substantiates the conjectures of the asymptotic behavior of the largest distance between consecutive primes: where γ is the Euler constant. The Hardy-Littlewood conjecture on the number of prime tuplets is investigated and the rationale for this conjecture is given, taking into account the fact that events are dependent on the fact that a large natural number is not divisible by primes. It also substantiates why the accuracy of this conjecture is not affected by another assumption about the probability of a natural number being prime, although such a probability does not exist. We consider the distribution of prime tuples using a mathematical model based on the Hardy-Littlewood conjecture. Keywords: probabilistic model, Hardy-Littlewood conjecture, Cramer conjecture, prime tuple, prime twins, asymptotic behavior of the greatest distance between consecutive primes, asymptotic law of primes, sequence density on the natural series interval, probability, dependent events, Mertens theorem, number of solutions comparisons, a complete system of residues, distribution of prime tuples, arithmetic function, random variable, independent random variables, mathematical expectation, variance, mean standard deviation, central limit theorem, asymptotic normal distribution. DOI: 10.25791/pfim.02.2020.1158 Pp. 39-45.