Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

An Observation on Distribution of Prime Numbers

Version 1 : Received: 14 June 2021 / Approved: 15 June 2021 / Online: 15 June 2021 (15:58:34 CEST)

How to cite: Bahrami, D. An Observation on Distribution of Prime Numbers. Preprints 2021, 2021060416. Bahrami, D. An Observation on Distribution of Prime Numbers. Preprints 2021, 2021060416.


In this research first, a sequence of properties called delta is assigned to each prime number and then examined. Deltas are only dependent on the distribution of prime numbers, so the results obtained for the delta distribution can be considered as a proxy for the distribution of prime numbers. The first observation was that these properties are not unique and different prime numbers may have the same value of delta of a given order. It was found that a small number of deltas cover a large portion of prime numbers, so by recognizing repetitive deltas, the next prime numbers can be predicted with a certain probability, but the most important observation of this study is the normal distribution of deltas. This research has not tried to justify the obtained observations and instead of answering the questions, it seeks to ask the right question.

Supplementary and Associated Material


Prime Number; Prime Numbers Distribution; Prime Number Generation; Normal Distribution


Computer Science and Mathematics, Probability and Statistics

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