The distribution of small gaps between successive primes

Brent, Richard P.

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The distribution of small gaps between successive primes

Date

1974

Authors

Brent, Richard P.

Abstract

For r ≧ 1 and large N, a well-known conjecture of Hardy and Littlewood implies that the number of primes p ≦ N such that p + 2r is the least prime greater than p is asymptotic to (Formula presented) where the Ar, k are certain constants. We describe a method for computing these constants. Related constants are given to 10D for r = 1(1)40, and some empirical evidence supporting the conjecture is mentioned.