**Anuraag Saxena and Abhimanyu Kumar**

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 30, 2024, Number 3, Pages 602–612

DOI: 10.7546/nntdm.2024.30.3.602-612

Full paper (PDF, 645 Kb)

## Details

### Authors and affiliations

Anuraag Saxena

*Department of Electronics and Communication Engineering,
Thapar Institute of Engineering and Technology
Patiala, Punjab 147004, India*

Abhimanyu Kumar

*Department of Electrical and Instrumentation Engineering,
Thapar Institute of Engineering and Technology
Patiala, Punjab 147004, India*

### Abstract

The degree of insulation of a prime is defined as the largest interval around within which no other prime exists. A prime is classified as insulated if its degree of insulation is greater than that of its neighbouring primes. This leads to the emergence of a new sequence, known as the insulated primes, which starts with 7, 13, 23, 37, 53, 67, 89, 103, 113, 131, 139, 157, 173, 181, 193, 211, 233, 277, 293, and so on. This paper explores several properties and intriguing relationships concerning the degree of insulation, and includes a brief heuristic study of the insulated primes. Finally, the reader is left with a captivating open problem.

### Keywords

- Special prime sequences
- Prime gaps

### 2020 Mathematics Subject Classification

- 11A41
- 11K31

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### Manuscript history

- Received: 23 June 2023
- Revised: 27 May 2024
- Accepted: 1 October 2024
- Online First: 24 October 2024

### Copyright information

Ⓒ 2024 by the Authors.

This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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## Cite this paper

Saxena, A., & Kumar, A. (2024). Insulated primes. *Notes on Number Theory and Discrete Mathematics*, 30(3), 602-612, DOI: 10.7546/nntdm.2024.30.3.602-612