Applied Physics and Mathematics Annotation << Back ESTIMATION OF THE ACCURACY FOR HARDY&#63162;LITTLEWOOD (ABOUT K&#63162;TUPLE) AND BATEMAN&#63162;HORN CONJECTURES V.L. VOL’FSON This paper shows that one can use only probabilistic estimation in many cases for the analysis of the distribution of primes in the natural numbers and arithmetic progression, and also to study the distribution of the prime tuples and the prime values of the polynomials in the natural numbers. The author generalized the probabilistic Cramer’s model to describe Hardy-Littlewood (about k-tuple) and Bateman-Horn conjectures. Probabilistic models for the estimation of the accuracy of these conjectures are constructed in the article. The author proved performance of the central limit theorem in the form of Lyapunov for the constructed probabilistic models. He found and proved the probabilistic estimates of the accuracy for Hardy-Littlewood (about k-tuple) and Bateman-Horn conjectures and showed the validity of these estimates at various examples. Keywords: probabilistic model, generalized Cramer’s model, random variable, central limit theorem in the form of Lyapunov, asymptotic normal distribution, probability estimates, prime numbers, k-tuple, twin primes, Hardy-Littlewoods conjecture, Bateman-Horn conjecture. Contacts: E-mail: znakvicvolf@mail.ru Pp. 51-57.