Science and Education Publishing
American Journal of Applied Mathematics and Statistics
2333-4576
2
2
2014
02
21
Series Primes in Binary
60
65
EN
P.M.
Mazurkin
Doctor of Engineering Science, Academician of RANS, member of EANS, Volga Region State Technological University, Russia
AJAMS2014222
10.12691/ajams-2-2-2
2014
02
08
2014
02
15
2014
02
21
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.