Geodesic
Using Bonse's inequality to find upper bounds on prime gaps
Journal of integer sequences, Tome 10 (2007) no. 3
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.
Classification : 11B05, 11B99
Keywords: bonse's inequality, cramér's conjecture, prime difference function, prime gap 
@article{JIS_2007__10_3_a4,
     author = {Betts,  Robert J.},
     title = {Using {Bonse's} inequality to find upper bounds on prime gaps},
     journal = {Journal of integer sequences},
     year = {2007},
     volume = {10},
     number = {3},
     zbl = {1140.11004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2007__10_3_a4/}
}
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Betts,  Robert J. Using Bonse's inequality to find upper bounds on prime gaps. Journal of integer sequences, Tome 10 (2007) no. 3. http://geodesic.mathdoc.fr/item/JIS_2007__10_3_a4/