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Applied Physics and Mathematics Annotation << Back
ESTIMATION OF THE ACCURACY FOR HARDYLITTLEWOOD
(ABOUT KTUPLE) AND BATEMAN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. |
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