The Distribution of Small Gaps Between Successive Primes
The Distribution of Small Gaps Between Successive Primes
For $r \geqq 1$ and large N, a well-known conjecture of Hardy and Littlewood implies that the number of primes $p \leqq N$ such that $p + 2r$ is the least prime greater than p is asymptotic to \[ \int _2^N {\left ( {\sum \limits _{k = 1}^r {\frac {{{A_{r,k}}}}{{{{(\log …