The distribution of small gaps between successive primes

21. R. P. Brent, The distribution of small gaps between successive primes, Mathematics of Computation 28 (1974), 315-324. MR 48#8356. Tables deposited in Mathematics of Computation UMT file and reviewed by Daniel Shanks, ibid, 331-332.

Abstract: dvi (2K), pdf (81K), ps (28K).

Paper: pdf (744K).

Review by Shanks of tables deposited in UMT file: pdf (170K).

Related, previously unpublished tables (dated 1 January 1970): pdf (604K).
[These are not the tables reviewed by Shanks.]


For r > 0 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 an integral involving certain constants Ar,k (see the dvi, ps or pdf version of the abstract for details). 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.

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