=ADD=
=reftype=
14
=number=
02-17
=url=
ftp://ftp.risc.uni-linz.ac.at/pub/techreports/2002/02-17.ps.gz
=year=
2002
=month=
07
=author=
Athale; Rahul
=title=
Verifying the Jumping Champion Conjecture
=abstract=
In this paper, we present the results of computational
verification of the jumping champion conjecture made by Odlyzko
et. al. in the paper \textit{Jumping Champions.} They have
given heuristics and  computational results for two intervals
of size $10^7,$ claiming that $210$ takes over as jumping
champion from $30$ somewhere between $10^{425}$ and
$10^{426}.$ In one of those two intervals, starting from
$10^{450}, 210$  was not a dominant gap. This motivated us to
verify the conjecture computationally. We considered intervals 
of size $10^7$ starting from $10^{410}, 10^{420}, \ldots,
10^{550}$ and in many of them $210$ did not appear as a
dominant gap.  Therefore we continued our experiments with
intervals of size $10^8.$ We present the results of these
experiments. We used computer algebra system Mathematica
(Mathematica is a product of Wolfram Research, Inc.) for the
computation.
=sponsor=
 .  
=note=
This paper will be presented in the Workshop on Computational Number Theory during the conference "Foundations of Computational Mathematics" (FoCM'02) at the IMA, University of Minnesota, Minneapolis, MN, USA, 5-14 August 2002.
=keywords=
prime gap, jumping champion