# The path to recent progress on small gaps between primes

@article{Goldston2007ThePT, title={The path to recent progress on small gaps between primes}, author={D. A. Goldston and Janos Pintz and C. Y. Yildirim}, journal={arXiv: Number Theory}, year={2007} }

We present the development of ideas which led to our recent find- ings about the existence of small gaps between primes.

## 13 Citations

Strings of congruent primes in short intervals

- Mathematics, PhilosophyJ. Lond. Math. Soc.
- 2011

It is proved that if (q, a )=1, then there are infinitely many pairs pr,p r+1 such that pr ≡ pr-1 ≡ a mod q and pr+1 − pr <� log pr.

An Overview of Sieve Methods

- Mathematics
- 2010

An overview of the power of Sieve methods in number theory meant for the non-specialist is provided.

The Goldston-Pintz-Yildirim sieveand some applications

- Mathematics
- 2013

The twin prime conjecture - that there exist infinitely many pairs of "twin primes" p, p + 2 - is among the most famous problems in number theory. In 2005, Goldston, Pintz and Yildirim (GPY) made a…

Small gaps between primes

- Mathematics
- 2007

AbstractCombining Goldston-Yildirim’s method on k-correlations of the truncated von Mangoldt function with Maier’s matrix method, we show that $$
\Xi _r : = \lim \inf _{n \to \infty } \tfrac{{p_{n +…

Towards a Proof of the Twin Prime Conjecture

- Mathematics
- 2018

Introduction: All primes greater than or equal to five are of the form 6j –1 or 6j +1. m =1 to n ∏ Pm = Jn is the product of the first n primes. The number of (6j –1, 6j +1) pairs with no factor less…

Distribution of prime numbers by the modified chi-square function

- Mathematics
- 2015

The statistical distribution of prime numbers represents an open problem in number theory still nowadays. The methodology of experimental mathematics has not yet been attempted in this field, thus…

Appendix A : Measure Theory

- Mathematics
- 2014

Complete treatments of the results stated in this appendix may be found in any measure theory book; see for example Parthasarathy [281], Royden [321] or Kingman and Taylor [195]. A similar summary of…

Séries de Dirichlet à deux variables et distribution des valeurs de fonctions arithmétiques

- Mathematics
- 2009

Nous traitons deux problemes lies aux series de Dirichlet. Nous etudions d'abord le prolongement analytique d'une certaine classe de series de Dirichlet a deux variables: g(s_1,s_2,a,r) = somme_d=1…

Levels of Distribution and the Affine Sieve

- MathematicsAnnales de la Faculté des sciences de Toulouse : Mathématiques
- 2014

This article is an expanded version of the author's lecture in the Basic Notions Seminar at Harvard, September 2013. Our goal is a brief and introductory exposition of aspects of two topics in sieve…

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