I am a one person company (OPC) that does research in both cryptography and cryptanalysis with the aim to create new products and/ or services.
Pattern among the prime numbers.
Number theorists have long questioned why primes seem to be scattered randomly among the integers, with no apparent pattern. In fact, every method and analysis employed to search for possible correlations in and between primes has revealed very little with respect to the underlying nature of their distribution.
Here, we propose a binary-coded decimal (BCD) representation for all positive integers and demonstrate that the resulting infinite pattern is a fractal. We prove that prime numbers follow a schematic (with respect to the twin primes) distribution within the self-similar structures of the above fractal binary pattern.
It is shown that visualization is a valid technique to probe into complex systems and helps towards the emergence of new mathematical methodologies. This idea has unexpectedly revealed the interdisciplinary nature of prime numbers by bringing together such apparently diverse disciplines as discrete mathematics, fractal geometry and number theory.