Related papers: Some history about Twin Prime Conjecture

We prove some theorems which give sufficient conditions for the existence of prime numbers among the terms of a sequence which has pairwise relatively prime terms.

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…

In this fact sheet we give some preliminary research results on the Bayesian Decision Theory. This theory has been under construction for the past two years. But what started as an intuitive enough idea, now seems to have the makings of…

This article describes the history of information retrieval on personal document collections.

This document seeks to prove there are infinitely many primes whose difference is 2, referred to as twin prime pairs. This proof's methodology involves constructing a function that approximates the number of positive integers, less than a…

The idea of generating prime numbers through sequence of sets of co-primes was the starting point of this paper that ends up by proving two conjectures, the existence of infinitely many twin primes and the Goldbach conjecture. The main idea…

We prove that there are infinitely often pairs of primes much closer than the average spacing between primes - almost within the square root of the average spacing. We actually prove a more general result concerning the set of values taken…

Prime number multiplet classifications and patterns are extended to negative integers. The extension from prime numbers to single prime powers is also studied. Prime number septets at equal distance are given. It is also shown that each…

The said paper [2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is with gaps.

Prime numbers have attracted the attention of mathematiciansand enthusiasts for millenniums due to their simple definition and remarkable properties. In this paper, we study primorial numbers (the product of the first prime numbers) to…

Classifications of twin primes are established and then applied to triplets that generalize to all higher multiplets. Mersenne and Fermat twins and triplets are treated in this framework. Regular prime number multiplets are related to…

This paper is meant as a contribution to the often debated subject of how to combine data which appear to be in mutual disagreement. As a practical example, the epsilon-prime/epsilon determinations have been considered.

We propose new conjectures about the relationship between the principal blocks of finite groups for different primes and establish evidence for these conjectures.

This is a survey of recent advances in commutative algebra, especially in mixed characteristic, obtained by using the theory of perfectoid spaces. An explanation of these techniques and a short account of the author's proof of the direct…

Prediction is a complex notion, and different predictors (such as people, computer programs, and probabilistic theories) can pursue very different goals. In this paper I will review some popular kinds of prediction and argue that the theory…

I exemplify part of my recent work on the upper halfplane.

The story on the early days of the Quantum Ergodic Theorem. Alternative proof, underlying heuristics, physical analogies and interpretations.

I briefly review the numerical evidence, some old and some quite recent, in favor of the center vortex theory of confinement.

For integers x and k, let T(x;2k) denote the number of twin prime pairs (p,p+2k) with a distance 2k<=2x**0.5 and p<=x (not p+2k<=x). Let Tg(x;2x**0.5) denote the average of T(x;2k) for all 2k<=2x**0.5. Logically, T(x;2k) should be a…

General considerations on the Equivalence conjectures and a review of few mathematical results.