Related papers: On the Twin Prime Conjecture

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 the paper, there are new found methods to determine the range of every exceptional element in exceptional set, we can solve Twin primes problem and Goldbach Conjecture problem basically.

We report the results of our empirical investigations on the Bateman-Horn conjecture. This conjecture, in its commonly known form, produces rather large deviations when the polynomials involved are not monic. We propose a modified version…

Probably we have observed a new simple phenomena dealing with approximations to two real numbers.

Starting from the first Hardy-Littlewood conjecture some topics will be covered: an empirical approach to the distribution of the twin primes in classes mod(10) and a simplified proof of the Bruns theorem . Finally, it will be explored an…

Some recent developments in the heavy quark theory are briefly reviewed. The main emphasis is put on interrelation between HQET and OPE. The notion of duality and deviations from duality are discussed in detail.

Following an idea of Rowland we give a conjectural way to generate increasing sequences of primes using algorithms involving the gcd. These algorithms seem not so useless for searching primes since it appears we found sometime primes much…

Two conjectures recently proposed by one of the authors are disproved

We show that the abc Conjecture implies the Weak Diversity Conjecture of Bilu and Luca.

Some observations on the Wu-Sprung potential.

We resolve the function field analogue of the conjecture concerning distribution of twin primes in arithmetic progression.

In this paper, we point out that the definition of weak tracial approximation can be improved and strengthened. An example of weak tracial approximation is also provided.

This paper introduces a new method to find the next prime number after a given prime ${P}$. The proposed method is used to derive a system of inequalities, that serve as constraints which should be satisfied by all primes whose successor is…

We have already conjectured 2 important guesses regarding Hypo-Lie algebra and modular simple Lie algebra. We would like to attach 2 important guesses more to this conjecture. Such new guesses are related to the Steinberg module.

In the proposed matrix primes, through which one can readily generate a sequence of primes. The paper also proposes a number of theorems proved by which an infinite number of prime numbers twins

Numerical evidence suggests that for only about $2\%$ of pairs $p,p+2$ of twin primes, $p+2$ has more primitive roots than does $p$. If this occurs, we say that $p$ is exceptional (there are only two exceptional pairs with $5 \leq p \leq…

In this paper we consider the remaining cases of Hebey-Vaugon conjecture.

Six conjectures on pairs of consecutive primes are listed in this paper, together with examples for each case.

We present a history of the Baum-Connes conjecture, the methods involved, the current status, and the mathematics it generated.

In this note, we state various generalisations of the Nakano vanishing theorem under weak positivity assumptions, and compare them with the known results.