Number Theory

    

Additive Walks on Natural Numbers and Proof of Twin and D-Primes Conjectures

Authors: Gregory M. Sobko

An additive model of random walks on set of natural numbers is applied to analyze the probability distribution of gaps, that is differences d = p’- p, between consecutive prime numbers p and p'. The well-known fact is that gaps between consecutive primes can be as small as 2 (for twin primes) and arbitrary large. This work is concerns with sets DP(d) of primes with gaps d (called d-primes), where d is an even number. For DP(2) we have a set of twin primes, with the unproven conjecture that DP(2) is an infinite set. We provide some statistical analysis for the frequency distribution of d-primes. The main result of this work is the proof that DP(d) is infinite set for every even d. The proof is based on modified Cramér’s probabilistic model for the distribution of prime numbers. This method has been discussed in detail in the author’s previous preprint [1].

Comments: 10 Pages.

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Submission history

[v1] 2021-10-11 19:54:59

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