@article{Cutter2001,
author={P. Cutter},
title={Finding prime pairs with particular gaps},
abstract={By a prime gap of size $g$, we mean that there are primes $p$ and $p+g$
such that the $g-1$ numbers between $p$ and $p+g$ are all composite. It
is widely believed that infinitely many prime gaps of size $g$ exist for
all even integers $g$. However, it had not previously been known whether
a prime gap of size $1000$ existed. The objective of this article was to
be the first to find a prime gap of size $1000$, by using a systematic
method that would also apply to finding prime gaps of any size. By this
method, we find prime gaps for all even integers from $746$ to $1000$,
and some beyond. What we find are not necessarily the first occurrences
of these gaps, but, being examples, they give an upper bound on the first
such occurrences. The prime gaps of size $1000$ listed in this article
were first announced on the Number Theory Listing to the World Wide Web
on Tuesday, April 8, 1997. Since then, others, including Sol Weintraub
and A.O.L. Atkin, have found prime gaps of size $1000$ with smaller integers,
using more ad hoc methods. At the end of the article, related computations
to find prime triples of the form $6m+1$, $12m-1$, $12m+1$ and their application
to divisibility of binomial coefficients by a square will also be discussed.},
journal= mc,
volume= 70,
year= 2001,
pages={1737--1744},
number= 235 ,
mrnumber={2002c:11174}
}
