Zagier [4] showed using elementary methods that π(n), the number of primes less than or equal to n, can be bounded by 2 3 n logn < π(n) < 1.7 n logn . His proof, which used strong induction and… Expand

2019 XIth International Scientific and Practical Conference on Electronics and Information Technologies (ELIT)

2019

The analysis of the probabilistic approach to solving the problem of the distribution of primes in the generalized Artin's hypothesis is given. The foundations of a computer approach to solving… Expand

It is known that prime numbers occupy specific geometrical patterns or moduli when numbers from one to infinity are distributed around polygons having sides that are integer multiple of number 6. In… Expand

We give a review of the rigorous results on the gaps between consecutive primes. Next we present heuristic arguments leading to the formula for the number of pairs of consecutive primes pn, pn+1 < x… Expand

While the prime numbers have been subject to mathematical inquiry since the ancient Greeks, the accumulated effort of understanding these numbers has - as Marcus du Sautoy recently phrased it - 'not… Expand

This work is devoted to the theory of prime numbers. Firstly it introduced the concept of matrix primes, which can help to generate a sequence of prime numbers. Then it proposed a number of theorems,… Expand

This research paper presents the results of a study on the application of extended analytic continuation to locate the non-trivial zeros of the Riemann Hypothesis.