Related papers: Some history about Twin Prime Conjecture

A review is presented of the origin and development of the atomic hypothesis from antiquity till about the first millennium of the common era.

This paper has been withdrawn by the author due to the version of [A complete proof of Hamilton's conjecture] at arXiv:1008.1576

New cases of the multiplicity conjecture are considered.

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

In this article, we investigate how Euler might have been led to conjecture the Prime Number Theorem, based on what he knew. We also speculate on why he did not do so.

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…

Can machines know what twin prime is? From the composition of this phrase, machines may guess twin prime is a certain kind of prime, but it is still difficult to deduce exactly what twin stands for without additional knowledge. Here, twin…

In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.

Several conjectural continued fractions found with the help of various algorithms are published in this paper.

We give some results and conjectures about recurrence relations for certain sequences of binomial sums.

This paper describes a method used to construct infinitely many probable counterexamples of the abc conjecture over the rational integers.

In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.

The earlier history of two--photon physics is reviewed.

This paper has been withdrawn by the author because Conjecture 1 is false. Please see arXiv:0901.2093 for a justification that Conjecture 1 is false. The other main results are also available from the above URL.

Comparative prime number theory is the study of the {\em{discrepancies}} of distributions when we compare the number of primes in different residue classes. This work presents a list of the problems being investigated in comparative prime…

The Polignac's Conjecture, first formulated by Alphonse de Polignac in 1849, asserts that, for any even number M, there exist infinitely many couples of prime numbers P, P+M. When M = 2, this reduces to the Twin Primes Conjecture. Despite…

In the present work the existence of some patterns of primes is shown which generalize the celebrated result of Green and Tao according to which there are arbitrarily long arithmetic progressions in the sequence of primes

All priors are not created equal. There are right and there are wrong priors. That is the main conclusion of this contribution. I use, a cooked-up example designed to create drama, and a typical textbook example to show the pervasiveness of…

We survey results about prime number races, that is, results about the relative sizes of prime counting functions $\pi_{q,a}(x)$, with $q$ fixed and $a$ varying. In particular, we describe recent work by the authors on these problems.

Dickson conjectured that a set of polynomials will take on infinitely many simultaneous prime values. Later others, such as Hardy and Littlewood, gave estimates for the number of these primes. In this article we look at this conjecture,…