Number Theory

    

The Cyclic Variation in the Density of Primes in the Intervals Defined by the Fibonacci Sequence

Authors: J. S. Markovitch

The Riemann R-function can be used to estimate the number of primes in an interval, where its accuracy is affected by the interval to which it is applied. Here, the successive intervals defined by the Fibonacci sequence will be shown to cause more cycles of R-function over- and under-estimation of primes than any of a large landscape of related sequences (calculations were continued up to one billion). The size of this landscape suggests that a special relationship exists between the Fibonacci sequence and the distribution of primes.

Comments: 14 Pages.

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[v1] 2013-12-02 13:19:11

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