Primes in tuples III: On the difference pn+v-pn

Abstract

In the present work we prove a new estimate for lim infn → ∞ where pn denotes the nth prime. Combining our recent method which led to δ1= 0 with Maier's matrix method, we show that δv We also extend the result to primes in arithmetic perogressions where the modulus can tend slowly to inflnity as a function of pn.