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Using Bonse's Inequality to Find Upper Bounds on Prime Gaps
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Robert J. Betts

University of Massachusetts, Lowell

One University Avenue

Lowell, MA 01854

USA

**Abstract:**

One can apply Bonse's inequality to points on the real line to find an
upper bound on any prime gap, including both for first occurrences and
for maximal prime gaps. However, such a result is neither as fine as
the upper bound found by Mozzochi, nor as fine as the lower bound
obtained by Rankin for maximal prime gaps.
Without deep sieve methods, such as those
used by Maier and Pomerance to compute a lower bound for maximal prime
gaps, we show one can
use Bonse's inequality to arrive at an upper bound for any given prime
gap without intricate derivations for any real constants.

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(Concerned with sequence
A001223.)

Received January 30 2007;
revised version received April 13 2007.
Published in *Journal of Integer Sequences*, April 13 2007.

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