Related papers: Finding a Widely Digitally Delicate Prime
Making use of covering systems and a theorem of D. Shiu, the first and second authors showed that for every positive integer $k$, there exist $k$ consecutive widely digitally delicate primes. They also noted that for every positive integer…
Tao has shown that in any fixed base, a positive proportion of prime numbers cannot have any digit changed and remain prime. In other words, most primes are "digitally delicate". We strengthen this result in a manner suggested by Tao: A…
We show that for every positive integer $k$, there exist $k$ consecutive primes having the property that if any digit of any one of the primes, including any of the infinitely many leading zero digits, is changed, then that prime becomes…
This is a survey article outlining what is known about absolute primes.
We introduce extremely symmetric primes and provide some elementary properties of these.
In this paper we present some observations about the well-known Goldbach conjecture. In particular we list and interpret some numerical results which allow us to formulate a relation between prime numbers and even integers. We can also…
The complexities of today's materials simulations demand computer codes which are both powerful and highly flexible. A researcher should be able to readily choose different geometries, different materials and different algorithms without…
I give some claims on primorial prime numbers for interested readers in number theory.
We study a special set of constellations of primes generated by twin primes.
We present a new, elementary, dynamical proof of the prime number theorem.
Recently we have introduced a novel characterisation of the distribution of twin primes that consists of three essential elements. These are: that the twins are most naturally viewed as a subsequence of the primes themselves, that the…
We present a simple, closed formula which gives all the primes in order. It is a simple product of integer floor and ceiling functions.
This paper investigates prime and co-prime integer matrices and their properties. It characterizes all pairwise co-prime integer matrices that are also prime integer matrices. This provides a simple way to construct families of pairwise…
A discrete map based on the sum of an integer's distinct primes factors and the sum of its other factors is defined and its iteration is studied.
This paper describes some of the ideas used in the development of our work on small gaps between primes.
In this article, we consider the structure of graded rings, not necessarily commutative nor with unity, and study the graded weakly prime ideals. We investigate the graded rings in which all graded ideals are graded weakly prime. Several…
A (positive definite and integral) quadratic form is said to be $\textit{prime-universal}$ if it represents all primes. Recently, Doyle and Williams in [2] classified all prime-universal diagonal ternary quadratic forms, and all…
We present a new algorithm for computing the first discrete homology group of a graph. By testing the algorithm on different data sets of random graphs, we find that it significantly outperforms other known algorithms.
We present a variety of prime-generating constructions that are based on sums of primes. The constructions come in all shapes and sizes, varying in the number of dimensions and number of generated primes. Our best result is a construction…
In this paper, we establish some theorems on the distribution of primes in higher-order progressions on average.