Primes in Tuples II

2007/10/15 by D. A. Goldston, J. Pintz, Goldston, D. A. +3 · 1 citation
Mathematics · #11N05 #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0710.2728

openalex publication_date 2007/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 on by the differences between primes.

Citations

• Primes in arithmetic progressions to large moduli

Cited by

• A Friendly Intro to Sieves with a Look Towards Recent Progress on the\n Twin Primes Conjecture

Related

• Primes in Tuples I
• Primes in Tuples IV: Density of small gaps between consecutive primes
• Distribution of Large Gaps Between Primes
• Small Gaps Between Primes I
• On the differences between consecutive prime numbers, I