Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Successive Addition of Digits of an Integer Number: On Properties and Role in Studying Distribution of Primes

Version 1 : Received: 18 June 2020 / Approved: 21 June 2020 / Online: 21 June 2020 (14:52:12 CEST)
Version 2 : Received: 12 August 2020 / Approved: 14 August 2020 / Online: 14 August 2020 (03:44:15 CEST)

How to cite: Khare, M.; Chitta, K. Successive Addition of Digits of an Integer Number: On Properties and Role in Studying Distribution of Primes. Preprints 2020, 2020060276. https://doi.org/10.20944/preprints202006.0276.v2 Khare, M.; Chitta, K. Successive Addition of Digits of an Integer Number: On Properties and Role in Studying Distribution of Primes. Preprints 2020, 2020060276. https://doi.org/10.20944/preprints202006.0276.v2

Abstract

Successive-addition-of-digits-of-a-number(SADN) refers to the process of adding up the digits of an integer number until a single digit is obtained. Concept of SADN has been occasionally identified but seldom employed in extensive mathematical applications. This paper discusses SADN and its properties in terms of addition, subtraction and multiplication. Further, the paper applies the multiplication-property of SADN to understand the distribution of prime numbers. For this purpose the paper introduces three series of numbers -S1, S3 and S5 series- into which all odd numbers can be placed, depending on their SADN and the rationale of such classification. Extending the analysis the paper explains how composite numbers of the S1 and S5 series can be derived. Based on this discussion it concludes that even as the concept of SADN is rather simple in its formulation and appears as an obvious truism but a profound analysis of the properties of SADN in terms of fundamental mathematical functions reveals that SADN holds a noteworthy position in number theory and may have significant implications for unfolding complex mathematical questions like understanding the distribution of prime numbers and Goldbach-problem.

Keywords

Primes; Distribution of Primes; Primes and integers; Additive questions involving primes; Number representations

Subject

Computer Science and Mathematics, Logic

Comments (1)

Comment 1
Received: 14 August 2020
Commenter: Manish Khare
Commenter's Conflict of Interests: Author
Comment: The earlier/first version of the manuscript was not having the proofs of certain discussed properties of SADN. These proofs are discussed in the updated/revised/present version of the manuscript.
+ Respond to this comment

We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.

Leave a public comment
Send a private comment to the author(s)
* All users must log in before leaving a comment
Views 0
Downloads 0
Comments 1
Metrics 0


×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here.