Related papers: The twin prime conjecture
In the paper, the occurrence of zeros and ones in the binary expansion of the primes is studied. In particular the statement in the title is established. The proof is unconditional.
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…
We resolve the function field analogue of the conjecture concerning distribution of twin primes in arithmetic progression.
We give a more comrehensive treatment of Chen's double sieve and improve related constants in Goldbach's conjecture and the twin prime problem.
We study a special set of constellations of primes generated by twin primes.
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…
This note announces recent exciting progress on the frontier between algebraic topology and probability theory. It is intended for a journal which publishes such announcements (without an abstract, typically in Russian). A description of a…
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…
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.
Since the mathematicians of ancient Greece until Fermat, since Gauss until today; the way how the primes along the numerical straight line are distributed has become perhaps the most difficult math problem; many people believe that their…
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 of the more…
We study an extension of Montgomery's pair-correlation conjecture and its relevance in some problems on the distribution of prime numbers.
The aim of this note is a proof of a recent conjecture of Kellner concerning the number of distinct prime factors of a particular product of primes. The proof uses profound results from analytic number theory, such as Granville-Ramar\'{e}'s…
In this work we prove that the set of the difference of primes is a $\Delta_r^*$-set. The work is based on the recent dramatic new developments in the study of bounded gaps between primes, reached by Zhang, Maynard and Tao.
We describe recent advances in the study of random analogues of combinatorial theorems.
This article is the extended notes of my survey talk of Gersten's conjecture given at the workshop "Bousfield classes form a set: a workshop in a memory of Tetsusuke Ohkawa" at Nagoya University in August 2015. In the last section, I give…
New cases of the multiplicity conjecture are considered.
This is a survey article on the Hardy-Littlewood conjecture about primes in quadratic progressions. We recount the history and quote some results approximating this hitherto unresolved conjecture.
The talk contains a brief introduction string theory, followed by a discussion of some of the recent developments.
New exceptional (i.e. non-repeating) prime number multiplets are given and formulated in terms of arithmetic progressions, along with laws governing them. Accompanying repeating prime number multiplets are pointed out. Prime number…