@article{BH96,
author={R. C. Baker and G. Harman},
title={The difference between consecutive primes},
abstract={The main result of the paper is that for all large $x$, the interval $A=[x-x^{0.535},x]$
contains prime numbers. The most recent published result meeting rigorous
standards is due to Iwaniec and Pintz ($0.547\dots$ in place of $0.535$).
The idea is to begin with asymptotic formulas for sums over products such
as $pqm$ in $A$ where $p$ and $q$ run over primes in suitably restricted
intervals and $m$ over some set of integers. One then builds on these formulae
using the sieve method of Harman (`On the distribution of $\alpha p$ modulo
one' J. London Math. Soc. 27 (1983), 9--18), to obtain asymptotic formula
for sums of the type $$\sum_m \sum_n a_m b_n S(A_{mn}, z),$$ the number
$z$ being a positive power of $x$ depending on the size of $m$ and $n$.
From this point, the use of Buchstab's identity enables one to reach a
lower bound for the number of primes in $A$ of $c$ times the expected value.
Certain integrals in two and four dimensions must be bounded above, using
a computer calculation, in order to ensure a positive value of $c$.},
journal= plms,
volume= 72,
year= 1996,
pages={261--280},
mrnumber={96k:11111},
series= 3
}
