Primes in Tuples II

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.

35 pages

References in corpus (1)

• Higher correlations of divisor sums related to primes III: k-correlations

Cited by in corpus (6)

• Bounded prime gaps in short intervals
• Note on Prime Gaps and Zero Spacings
• Note On Prime Gaps And Very Short Intervals
• A Friendly Intro to Sieves with a Look Towards Recent Progress on the Twin Primes Conjecture
• Note On The Maximal Primes Gaps
• Properties and applications of the prime detecting function: infinitude of twin primes, asymptotic law of distribution of prime pairs differing by an even number