Insulated primes

Abstract

The degree of insulation of a prime $p$ is defined as the largest interval around it in which no other prime exists. Based on this, the $n$-th prime $p_n$ is said to be insulated if and only if its degree of insulation is higher than its neighboring primes. Consequently, a new special sequence emerges given as 7, 13, 23, 37, 53, 67, 89, 103, 113, 131, 139, 157, 173, 181, 193, 211, 233, 277, 293, and so on. This paper presents several properties and intriguing relations concerning degree of insulation and insulated primes. Finally, the reader is left with a captivating open problem.

arXiv comment11 pages, 7 figures