From saw@qcvaxa.acc.qc.edu Sat Jun 28 16:49:20 1997
Date: Sat, 28 Jun 1997 12:19:22 -0400
From: Sol Weintraub <saw@qcvaxa.acc.qc.edu>
To: NMBRTHRY@LISTSERV.NODAK.EDU
Subject: Prime gaps of size exactly 1000

Several recent postings listed prime gaps greater than 1000, but none of a
gap of exactly 1000.
The following 2 gaps are of size exactly 1000:

A gap of 1000 occurs near 1.0*10^51 after the prime:

     1007680433959245619392429620296326354948036597945187

and a gap of 1000 occurs  near 4.4*10^48 after the prime:

     4397520531997777107052961684797293978927491104897

These, in all likelihood, do not represent the first occurrences of gaps
of size 1000, but they do give an upper bound to Shanks' [1] question
as to where the first gap of size 1000 occurs.


Sol Weintraub
Queens College, City University of NY.

Reference,

[1] D. Shanks, On Maximal Gaps between Successive Primes, Math. Comp., 18,
pp. 646-651, 1964