Related papers: On the Twin Prime Conjecture

We discuss recent advances on weak forms of the Prime $k$-tuple Conjecture, and its role in proving new estimates for the existence of small gaps between primes and the existence of large gaps between primes.

We survey recent developments on the Restriction conjecture.

This article is a collected information from some books and papers, and in most cases the original sentences is reserved about twin prime conjecture.

We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.

This is an extension and background to a talk I gave on 9 October 2013 to the Brown Graduate Student Seminar, called `A friendly intro to sieves with a look towards recent progress on the twin primes conjecture.' During the talk, I mention…

This is an exposition of recent developments in the theory of bounded differences between primes. Readers are expected to be beginners of analytic number theory. The present text is a substantially improved and augmented version of the one…

We give an equivalent form of the Twin prime conjecture relating to a symmetric property that is observed for terms present in a certain sequence of arithmetic progressions defined for a pair of co-prime integers.

We discuss the (twisted) weak positivity theorem. We also treat some applications.

We adopt an empirical approach to the characterization of the distribution of twin primes within the set of primes, rather than in the set of all natural numbers. The occurrences of twin primes in any finite sequence of primes are like…

We give a counterexample to a recently conjectured variant of the Penrose inequality.

This is a survey on Kawaguchi-Silverman conjecture.

New cases of the multiplicity conjecture are considered.

In this paper, we give a survey of the recent develpoments of the DDVV conjecture.

We present a selection of known as well as new variants of the Sensitivity Conjecture and point out some weaker versions that are also open.

The twin primes conjecture is a very old problem. Tacitly it is supposed that the primes it deals with are finite. In the present paper we consider three problems that are not related to finite primes but deal with infinite integers. The…

In this survey article we outline the history of the twin theories of weak normality and seminormality for commutative rings and algebraic varieties with an emphasis on the recent developments in these theories over the past fifteen years.…

In this paper, we derive a more precise version of the Strong Pair Correlation Conjecture on the zeros of the Riemann zeta function under Riemann Hypothesis and Twin Prime Conjecture.

The twin prime conjecture asserts that there are infinitely many pairs of primes that differ by two. While recent advances have improved our understanding of bounded prime gaps, the conjecture remains unresolved. This paper refines the…

In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.

A recent heuristic argument based on basic concepts in spectral analysis showed that the twin prime conjecture and a few other related primes counting problems are valid. A rigorous version of the spectral method, and a proof for the…