Article citationsMore >>

Gashkov S.B. Number systems and their applications. M. MCCME, 2004. 52.

has been cited by the following article:

Article

Series Primes in Binary

1Doctor of Engineering Science, Academician of RANS, member of EANS, Volga Region State Technological University, Russia


American Journal of Applied Mathematics and Statistics. 2014, Vol. 2 No. 2, 60-65
DOI: 10.12691/ajams-2-2-2
Copyright © 2014 Science and Education Publishing

Cite this paper:
P.M. Mazurkin. Series Primes in Binary. American Journal of Applied Mathematics and Statistics. 2014; 2(2):60-65. doi: 10.12691/ajams-2-2-2.

Correspondence to: P.M.  Mazurkin, Doctor of Engineering Science, Academician of RANS, member of EANS, Volga Region State Technological University, Russia. Email: kaf_po@mail.ru

Abstract

To prove the famous Riemann hypothesis, that the real part of the root is always exactly equal to 1/2, a series of 500 and the other prime numbers has been converted from decimal to binary number system. At the same time was a clear non-trivial zeros. Any prime number can be represented as quantized into binary digital signal. Quantization step to not dilute a number of prime numbers is 1. Number of levels (binary digits) depends on the power of the quantized number of primes. As a result, we get two types of zeros - the trivial and nontrivial. Capacity of a finite number of primes must be taken based on the completeness of block incidence matrix. Average statistical indicator is a binary number, and influencing variable - itself a prime number. The binary representation allows to visualize and geometric patterns in the full range of prime numbers.

Keywords