## 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Related, previously unpublished tables (dated 1 January 1970):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.]

## Abstract

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*+2*r* is the least
prime greater than *p* is asymptotic to
an integral involving certain constants
*A*_{r,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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