A closed-form solution for the boundary of the flat state of an orthogonal cross section of contiguous surface geometry formed by the intersection of two cylinders of equal radii oriented in dual… Expand

We provide a brief explanation of the concept of prime numbers with prime subscripts. To this end, we refer the reader to the OEIS reference [1] on higher-order prime numbers, and to the paper [2].… Expand

One familiar with the Euler zeta function, which established the remarkable relationship between the prime and composite numbers, might naturally ponder the results of the application of this special… Expand

This research presents the results of a study on the existence and frequency distribution of the shell primes defined herein as prime numbers that result from the calculation of the "half-shell" of… Expand

In this paper, we analyze properties of special subsequences of prime numbers produced by the alternating sum of higher-order subsets of the primes. We also introduce a sieve which will generate… Expand

This research paper presents the results of a study on the application of extended analytic continuation to locate the non-trivial zeros of the Riemann Hypothesis.