In this work, a possible justification is delivered of the P.N.T. based on periodic binary sequences that are present in the characteristic function of the primes, with suggestions for future developments. Based on this analysis, preliminary versions of two novel methods for effectively estimating the prime number function (x) and the twin prime number function 2(x) are obtained, which are comparable with the estimations based on the natural logarithm. Finally, two remarkable consequences are delivered: the new approximations produce a satisfactory and intuitive explanation of the connection of the natural logarithm with the density of the primes and twin primes.
The distribution of the prime numbers: a novel approach linked to the Prime Number Theorem
2017
Abstract
In this work, a possible justification is delivered of the P.N.T. based on periodic binary sequences that are present in the characteristic function of the primes, with suggestions for future developments. Based on this analysis, preliminary versions of two novel methods for effectively estimating the prime number function (x) and the twin prime number function 2(x) are obtained, which are comparable with the estimations based on the natural logarithm. Finally, two remarkable consequences are delivered: the new approximations produce a satisfactory and intuitive explanation of the connection of the natural logarithm with the density of the primes and twin primes.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
