Related papers: On a sequence involving the prime numbers

The problem of integer partitions is addressed using the microcanonical approach which is based on the analogy between this problem in the number theory and the calculation of microstates of a many-boson system. For ordinary…

We obtain asymptotic results on the average numbers of Goldbach representations of an interger as the sum of two primes in different arithmetic progressions. We also prove an omega-result showing that the asymptotic result is essentially…

In this paper, we propose new sequential estimation methods based on inclusion principle. The main idea is to reformulate the estimation problems as constructing sequential random intervals and use confidence sequences to control the…

An elementary method for computing various prime sequences using the sequence of Farey sequences is described.

A large class of problems in sciences and engineering can be formulated as the general problem of constructing random intervals with pre-specified coverage probabilities for the mean. Wee propose a general approach for statistical inference…

We develop symbolic methods of asymptotic approximations for solutions of linear ordinary differential equations and use to them stabilize numerical calculations. Our method follows classical analysis for first-order systems and…

By means of a Fourier optimization framework, we improve the current asymptotic bounds under GRH for two classical problems in number theory: the problem of estimating the least quadratic non-residue modulo a prime, and the problem of…

For the Chebyshev-Stirling numbers, a special case of the Jacobi-Stirling numbers, asymptotic formulae are derived in terms of a local central limit theorem. The underlying probabilistic approach also applies to the classical Stirling…

In this paper, we propose a new primality test, and then we employ this test to find a formula for {\pi} that computes the number of primes within any interval. We finally propose a new formula that computes the nth prime number as well as…

The objective of this paper is to introduce an approach to the study of the nonasymptotic distribution of prime numbers. The natural numbers are represented by theorem 1 in the matrix form ^2N. The first column of the infinite matrix ^2N…

We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.

We study the integer sequence v_n of numbers of lines in hypersurfaces of degree 2n-3 of P^n, n>1. We prove a number of congruence properties of these numbers of several different types. Furthermore, the asymptotics of the v_n are described…

We study pairs of consecutive odd numbers through a straightforward indexing. We focus in particular on twin primes and their distribution. With a counting argument, we calculate the limit of an alternating sum that is equal to 1 which…

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…

On the assumption of the Riemann hypothesis, we give explicit upper bounds on the difference between consecutive prime numbers.

In this paper, we show a new upper bound of prime gaps, that is the gap between a prime number and its consecutive prime number. We show that the gap between a prime number $p_n$ and its consecutive prime number is not larger than…

We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any…

A "simple trace formula" is used to derive an asymptotic result for class numbers of complex cubic orders.

We obtain an asymptotic formula for the number of ways to represent every reduced residue class as a product of a prime and square-free integer. This may be considered as a relaxed version of a conjecture of Erd\"os, Odlyzko, and…

Let $p_{1}<p_2<... <p_{\nu}<...$ be the sequence of prime numbers and let $m$ be a positive integer. We give a strong asymptotic formula for the distribution of the set of integers having prime factorizations of the form…