The use of binary bands for the determination of Goldbach’s conjecture coincidences

GUSTAVO FUNES, DAMIÁN GULICH, LEOPOLDO GARAVAGLIA, MARIO GARAVAGLIA

Sociedad

Conferencia; M&D 2010 - VI Conferencia Internacional de Matemática y Diseño; 2010

Centro de Matemática y Diseño - Asociación Internacional de Matemática y Diseño

In our previous work we have discussed hidden symmetries among prime numbers using a graphical sieve superposing binary bands. These symmetries could be the key in conjectures such as Golbach and Polignac. In this work we shall take a deeper look at Golbach's conjecture and we will analyze the various ways of obtaining an even number as sum of two primes. This amount, which seems to be a growing succession, has certain local maximum and minimum for certain even numbers. In order to explain this we will analyze the behavior of the binary bands of multiples to try to predict which even numbers will have local maximum or minimum. We will see that the amount of coincidences for this particular conjecture seems to have a random form because of the seemingly random form of the prime number series itself. Although we will see the deterministic nature inside.